We had problems with constant ear infections with my son, also...
At one point, he was on a 3 week Therapeutic dose of an antibiotic (to get rid of any lingering infection), and was then going to go on a half-dose of antibiotic as a suppressive dose to try to keep from getting more infections...
Well, while he was on the 3 week therapeutic dose, he ended up with a double ear infection!
At that point, we were very tired of the constant ear infections, and called an ENT..... a week later, he had surgery to put in ventilation tubes.... (and... he STILL got ear infections!). Yes, even with the tubes, he got ear infections... (he was just about 14 months old at this point), so the doctor then put him on a nasal spray (something like flonase)...... at that point, the nasal spray really helped..
And yes, he did outgrow the ear infections.... by the time the tubes came out, he had pretty much outgrown the ear infections.... and now, at age 22, probably had maybe 1 or 2 ear infections since the tubes came out.
(Also... one time, he had a pretty severe sinus infection that, as the doctor described it, also drained out through the tear ducts..... so that may be the nasty eye boogers you are seeing.....)