ROTC is for becoming an officer, and is during college.
You could become an officer in the 101st if you go to airborne school.
Im not to sure about the asthma thing though.
If you enlist and volunteer for airborne and meet the physical requirements , then you would go to boot camp, mos training , then airborne school. If you pass airborne school you might be with the 101st or the 82nd airborne.
You could enlist, then later apply to try out for airborne, but volunteering during basic or getting it in your contract would be best.
So to be in the 101st or 82d means you have to go to airborne school, and have a job that allows you to go.
ROTC AGAIN IS A program you do when your in college to become an officer.
Good luck