My baby has a fever and a touch of diarrhea. Is that because he's teething?

It cannot be due to teething, but definitely due to the number of things that he is putting in his mouth to soothe his irritated gums. Make sure that you sterilise all his teethers and toys that he puts in his mouth as he can get a stomach infection. Give him carrot sticks and bread sticks to chew on, instead.