People with pneumonia can recover, even older people. With the right treatment of course and rest. 

It's normal to become breathless if you don't exercise, it doesn't mean something is wrong with you. I don't think it has something to do with weight, although surely if you are overweight you are pressuring the body more and thus it's easier to get breathless. 
Unless you suffer from some disease or something else that causes you to easily get breathless. 

Your doctor is only being thorough. Wait until you get the results back, it could be nothing, so you could be worrying in vain. 

It might just be anemia, or your lungs having to work harder because they have to support a larger body.  I'm not sure that there's any point to worrying until you know for sure.  You can cause yourself a lot of stress and then discover it's not something that's life-threatening.  However we can't always choose what we're going to feel, right?  So you might not have a choice about being worried, and that's normal too.

I find that it's easier to put worries to rest if you have a plan, and you take action.  If you're busy working on your problems you don't have as much brain function to spend on negative emotions.  Since your worries are health related, it's probably best to start there.  Although the problem with health is that there's a lot of conflicting info out there.  The basics are pretty straightforward for the general case -- eat in moderation, get a bit of exercise, avoid toxic people who make you feel like shit, get a good amount of sleep and try to minimize stress.  Of course all these things are easier said than done, so there's a lot of "get improvement fast" schemes or people become convinced that their way is the one true way and get super uptight about people doing anything else.

If you're recovering from lung disease and have a tendency to get breathless then I'd probably focus on eating healthy food in moderation first, getting enough regular sleep, and doing light exercise like walking outdoors.  Focus on setting up good habits rather than trying to overhaul your life in one go.  If you have mental health issues then consider talking to a therapist or support group.  Your profile says that you're having financial problems right now and that's going to add to your stress, but luckily walking is free and so is cutting down on food portions.  You don't have to spend money on health food, nobody ever died from having too little quinoa in their diet, y'know?  Just pay attention to calorie counts and if you have a choice between a little more and a little less then choose less more often.

Lung capacity is a thing that changes iirc, like with aerobic exercise, freediving, that sort of thing. If you've not been doing much to make use of it, are also obese, and then on top of that you got sick, then they might have just not had much capacity to lose.

flu is bad this year maybe you have a touch of that

Nah, it's not anything to really worry about. When you have a lung infection it's normal for you to have some problems for a few months after. Your lungs are damaged. It's going to make you get out of breath really fast. The lung function test is really just to make sure that they're healing. 

It has nothing to do with your age, it's just something they do if your lungs have taken some damage. Most of the time they can heal on their own, but sometimes there will be scarring or it will lead to COPD or something, and if that's going to happen it's best to find out as early as possible since they can be countered with breathing therapy and medications before they become a major problem. 

If you went in for a routine checkup and they wanted a lung function test, then that might be something to worry about. But in this case it's just standard follow up for an infection. 

And respiratory tests are really simple. It's nothing to worry about, not like they'll be poking you with needles or hooking you up to invasive machines. There are a few different ones but it boils down to breathing into a tube thing. 

If you're worried that you might be having problems getting enough air, you can buy a pulseox monitor for about $25 at most pharmacies. It's the little thing doctors clip onto your finger, and it just monitors your pulse and blood oxygen level. If you're worried about heart or lung function it's a really useful thing to have. 

I had a couple really bad lung infections and blood clots that killed about half my lung tissue. It took about eighteen months to get back to more or less normal from that. That was a pretty extreme case, I had to be in the hospital for awhile. I got out of breath super easy for maybe four or five months, after that it was just when I was exerting myself or singing or there was lots of dust or pollen in the air.  

lol After that I managed to get a couple super nasty viruses, my lungs aren't super great. But they're good enough for me to sing and talk on stage loudly enough for people to hear me without a mic in a small auditorium. 

As to being breathless in general, if your body weight is low and you don't get much exercise then that's normal- not healthy, but to be expected. Posture and bad breathing habits can also make you get out of breath even though there is nothing 'wrong' with you. Sitting in a hunched position or otherwise cramping your chest, tightness in your back or core, and anxiety or just plan habit can make you take shallow breaths. Breathing is automatic, but you usually control the exact way you do it. 

So sometimes when you tend to be out of breath it has to do with something physical or psychological that you have some control over. 

I say go with what the doctor says. Chances are its the flu, as Chibikki-ikki said, it can sometimes irritate your lungs. (it's happened to me before. not a fun time but it doesn't last forever.)

And don't worry. If they have to do a test, remain calm and don't panic. Relax and think about something else while the test happens.

Follow the doctor's orders (or suggestions) as others here imply. Whether you should worry or not depends on the test results - that's the reason you should get them asap.

Best case you catch flu, flu sometimes irritate your lungs, especially if your immune system is already weak
Worst case you catch TBC, while TBC sounds scary, it usually easy to diagnose and easy to cure with modern medication

Best suggestion is to follow whatever your doctor's trying to say
and no you shouldn't be worry,
I suffer COPD but I turn out fine and pulmonary function test is not really that scary too,
last advice, don't panic when you do the test since panic will mess up the result

If the doctor suggests it then I think it would be best to accept. Least you'll find out what you got and how they can try and cure it.