Isabel (age 6) had 4 strep infections in one year, and also was having episodes where she'd stop breathing in the middle of the night and then gasp because the tonsils were so enlarged.
I would go to a good ENT (ear-nose-throat) doctor in your area (if you live in Atlanta I can recommend a fantastic one). Most pediatricians won't tell you to go to an ent, even if your kid's getting strep over and over again.

But the ENT will tell you definitively if the tonsils and adenoids are enlarged, what percentage they are obstructing the airway (Isabel's airway was over 70% obstructed, gawd.) and what your options are.
Again, I'd *really* recommend a specialist for this. Everyone I know who's asked me about it has had their pediatrician blow it off.
Once she had her tonsils and adenoids out, she grew an inch and a half in the first month post surgery, and the issues she was having with her attention span disappeared.
The ENT felt that both issues were because she was not getting any sort of good deep sleep because of the trouble breathing, and when you don't get deep, uninterruped sleep you can't concentrate during the day, and you don't grow well.
Strep sucks. Oddly enough, my younger daughter has had it once in her entire five years (madly knocking wood here!).