15 Month Old Ongoing Cough/Runny Nose HELP

My daughter is 15 months old now and has had a runny nose since late Feb/March. It goes from thick yellow to clear on and off throughout the days. On top of the nose constantly being congested she has now had a horrible cough for going into her 4th week this week. I've had her to her doctor numerous times to listen to her chest and he says it isn't in her chest just sounds worse than it is. He thinks she has had one cold after another and they are looping together. Is it possible for her to always be sick?? She was healthy as could be until she hit the year mark. She is in day care 3 days a week so I was expecting her to be sick but not have the continuous runny yellow nose and cough.
He doesn't think she needs a chest x ray and he doesn't think it's allergies. He said an allergist at this point can't test her til she is 3 yrs old anyhow for a true testing so there really isn't much they would do at this point.
He does think it could be connected with her teeth coming in and said some kids are congested all the way until they are done teething.

Her personality is fine, she eats well, drinks well etc. She had a fever once or twice over the coarse of time that she has had this but for the most part doesn't run a fever either. Just a worried mom that doesn't know what to do at this point. Take her to an ENT, allergist, get a chest x ray or just let it run it's course. The doctor put her on Amoxicillin last Tuesday at her 15 month check up only because he noticed a little fluid in her one ear which was the first time for that. The medicine doesn't seem to be helping the nose or cough though and is almost empty.

[RImommy]

Im in this exact same situation with my 15 month old.  Im so frustrated and feel awful for my daughter.