I wouldn't worry too much - just know it may take a while to get medically cleared. I have a hx of asthma too. I did the original physical, writing on it (and having the physician write on it too) that I've completed half-marathons and triathlons with no problem and no medication (so have both you and the physician write your 8 mi/mile on yours). Make sure you also state that you no longer require medication (if that's true).
For the Navy, if the asthma was resolved when you were under 13 years of age you won't need a waiver. Unfortunately for me, I stopped taking meds before 13, but it wasn't on my record that I stopped, so I had to get a waiver.
After the original physical, I waited for quite a while to hear back from DoDMERB, and when I did they wanted a pre- and post- bronchodilator spirometry test (I think that's how you spell it). I'm told it's not bad, but don't take the test if you are sick! I don't think you can train for it. Here's the kicker - I wrote a nice formal letter to the waiver committee stating my case (grew out of it, stopped medication before 13 years of age, having completed X amount of activity without problems) and they gave me the waiver without any other question and I never had to take the test.
Now, your case may be different, but don't stress about it now, there's no point. Just try, it's all you can do. And make sure you stay in contact with Rebecca Patterson - you'll meet her at the interview. She was instrumental in me getting cleared! And she's super super nice and helpful!!
Good luck

and congrats on the interview!
😀
Edit: not knowing whether you're male or female, grotto's PRT score is correct, but for males. If you're female and under 25, the 1.5 mile passing time is 15:15 so you'd be more than good.