Teething or more?

I've been to the Dr 4 different times in a month... I even seen a second Dr for another opinion.

My son is 9 months old, He had a dry cough, and congestion, that has recently turned into excessive sneezing and Everytime he sneezes ALOT of snot comes out, and an excessive runny nose, He is teething, but Drs are saying teething doesn't cause these symptoms. He has had little to no fever, In the begining he had a fever one time. He has been given, Amoxicillin (which he's on his last couple doses now.) Nasal drops, and he has also had a rash that covered most of him, It looked alot like a heat rash, They first said it could have been eczema, but they decided after the second appointment it definitely was not and said it looked like his skin was irritated, maybe a skin allergy. They gave him steroids for that and it went away, but it did come back, not as bad, but it did. I wondered if the rash way my fault, maybe I was over dressing him. So I dressed him in lighter layers especially at night, or when he was in his car seat. Anyways, Did any of your children have these symptoms while getting their first teeth? He has his 2 bottom front teeth coming in, You can see them, He has been suffering for nearly a month. Idk what else to do, we are riding it out. He doesn't have a fever, but he is very irritable. I think the Drs are begining to think I'm a hypocondriac, I've had him there over and over. No new diagnosis. But NO answers 😭