2 year molar symptoms?

I know symptoms are varied per child. My 27 month old has had a cough/cold since the 7th. Acts completely fine though. The cough went away after 8-9 days but the runny nose and congestion stayed. Then 5 days later the cough started again. 2 days ago I saw her too molar poking through (which explains her grumpiness and neediness) and she wakes up saying owie owie.

Could a cough also be from teething? No fever. Nothing. Acts completely fine most of the time except for periods of WTF mood swings 😅 Thanks!