The nice thing about OTS is you don't go if you don't get a fixed wing pilot slot. Don't accept anything else. They will have you put three specialty codes on the application. Most put fixed wing, rotary wing and navigator. The other good deal about OTS is that if you wash out of UPT, you go home, not to some shoe clerk supply job in Korea. It may be tougher to get a slot, but it's worth it. ROTC is a bit of a crap shoot. If you don't get a pilot slot, you still owe them for the schooling.
BTW, who says you have asthma? I had a high blood sugar test once, didn't mean I had diabetes, just means I didn't fast like I was supposed too. How can you be sure you didn't just have a simple alergic (you don't have allergies either) reaction. I wouldn't bring up or put down anything on the application. As far as medical history, where is it written?