how can you tell if your baby is teething?

My son has been chewing on his hands for the past month ( hes 3 months old now), it's  not hungry chewing. He is putting his index finger or thumb in his mouth and chewing and sucking on it. He is drooling so much he wears a bib at all times! Yesterday when I was feeding him he pushed the bottle away with his hand and started chewing on his fingers again. People say to put your fingers in his mouth and feel his gums but I having done this yet and wouldn't know what to look for, any advice? ( in the picture he had a wee bit of conjunctivitis in his right eye but it's cleared up now)