So I broke my eardrum and I’m headed to basic training July 29th. Am I going to have a problem at reception?

Damn skippy you will have problems at Reception. So, IMHO and best advice: STOP!! DO NOT PASS GO!!! Contact your Recruiter STAT and notify them of the medical situation and also seek medical attention to get it checked out.

Yes, it will be a problem. You need to contact your recruiter about this ASAP. Going by your below response of what "someone" told you, in terms of not saying anything? Bad call on their part. I'll give you a highly likely hypothetical:

You do nothing about this. You report your reception BCT post and begin processing. It's not going to take long for the problem to be noticed and you force marched to Medical where it will be checked out and then the questions flow. By you saying you "broke" your eardrum, I am assuming it ruptured in some way? This will leave scarring that can be measured to a degree as to how long ago it happened and it is not something that goes unnoticed by a person. So this then presents prior knowledge that you did not report, because when you in process one of the many questions they WILL ask is: Has anything changed since you went to MEPS? Failure to report means that at BEST you get yanked from BCT, and get recycled WHEN your eardrum is healed. At worst you get chaptered out of the army and this gets annotated in your file making it harder for you to re-enlist.

You said this happened at the Recruit Sustainment Program. I take it that is run by recruiters who you attempted to tell? You already have taken your oath. Definitely Be sure to document with your doctors and your recruiter in case of future disabilities. Like one SSG said and you know it should heal and you will be okay but you have had multiple trauma to the eardrum so your doctors need to address that. Good luck!!!!