It could very well be teething. My son started the drooling and chewing on things at about 3-4 months, but we didn't see the first tooth until his 6 month checkup. By 10 months, we had eight teeth. Some babies just teeth earlier than others and it is all perfectly normal. I could always tell when my son was getting a tooth because he would constantly get the hiccups, start spitting up, become restless at night and fussy during the day. This would last for about three days, then we would have a new tooth...sometimes two! That is just how he did it. Evey baby is different.
We tried the teething tablets and orajel, but they didn't work. It just seemed to make him more mad. What did work was tylenol and frozen french fries (I put the fries in baggies, so he couldn't accidentally swallow some).