My son has a similar desire to join at 17, and will be in July. As far as the asthma, don't sweat it. The Auxiliary's restrictions are pretty straightforward: if you can do the job, you do the job. If you can't you can't. Allergy induced asthma wont prohibit you from joining. There's a certain responsibility that falls on the member to be honest with himself, and his/her shipmates with regard to medical issues.
With regard to our role, by statute, we are allowed to do almost any job the Gold Side can do with the exception of direct military action (warfighting), and law-enforcement. The additional restrictions are obvious - you cant be a rescue-swimmer or a C-130 pilot, and you're not going to command a cutter, etc... On the other hand, if you want to qualify to work with the active-duty on a small boat (there are people on this forum who do just that), or a Marine Safety Unit (I do this), you can.
Finding out about local flotillas is important, and talking to the members to see what unit best fits what you want to do is an important step in your success in the organization. You nee to be happy where you are. If you are operations oriented, try and find an operations oriented flotilla (you can work with any unit, but working with your home unit - with people you know and hopefully like is much more enjoyable).
My suggestion to you is visit a few flotilla meetings, see how the members interact, ask LOTS of questions, then decide where you'd like to hang your hat. You can transfer, but it is a bit of a hassle. Take the time to make the right decision. One other thing, VicNaz wrote a really good explanation of AUX physical fitness standards, much better than I outlined. Give it a read.
We're here to answer questions, so ask away. Good luck and welcome aboard!