asthma?

So how do I know if I have asthma? I have run/exercised all my life (yes I fell off the wagon many times where I wasn't doing it consistently). I enjoy running but can't remember back to my high school days when I was actually running a descent speed as to whether I had the problems I have now, or if it's just new.
I realize the best option is to go to a doctor to find out- but you all know the outrageous costs they charge just to walk in the door and my insurance isn't great right now.
Here's what's happening. I started training for a 1/2 marathon in January. So I got on a schedule running 4-5 times a week starting slow and shorter distances to getting faster and longer distances. In January I started at 5-8 miles per week at a 15min/mile pace. I am now averaging about 12-15 miles per week at around 11 to 11:30 min/mile pace. I did run my 1/2 marathon at the end of April and finished 2:58 (so 13:15 min/mile pace). What I find is I run pretty well for the first 3-5 miles. On longer runs, I finally have to stop and walk-not because of cramps but because I feel "heavy" and when I do stop, I'm breathing very heavy. I doesn't seem to take me long to recover and I can resume running but once I've walked, I then stop more during the run. and I find myself taking quick breaths now and then through my mouth instead of nose like I need more air. When I run, I always feel congested and allergy (OTC) meds don't seem to help me running (they do help with normal day to day type allergy reactions).
As I've lost weight, I have been able to speed up and I know that if I lose the rest of the weight I need to, I will get faster yet (goal is to do 1/2 marathon with 10 min/mile pace. but somehow I think my breathing might be holding me back right now.

an example: I went running for just 2 miles the other night and my pace for the 1st mile was around 9:45. I ended with an average pace of 10:15 but was DYING when I finished. I was breathing so heavy it wasn't funny. My muscles seem to be fine, I never have any strain or cramps. I would love to get back to a 8:30min/mile pace for my average 3-5 mile runs. I just thought I would have made more "time" progress in the 6 months than I did. I realize cutting 4.5 min/mile is a big deal, but having been a runner, thought I'd make the time up faster than that. I realize I won't run like I did in high school, but I feel I'm really slow where I'm at for my age.