Three months is the normal age for babies to start teething. They can start popping out sometime soon, or your baby can teeth for months before ever getting one. Teething toys work great, as well as the teething bibs and blankets. My children ranged anywhere from as early as six months to as late as a year before they got their first tooth. 

Not rare at all, I work at a daycare and teething can generally start at 3 months or sometimes earlier, there are even some babies born where you can feel their little teeth buds right under their gums. I teach young toddlers and the best I find in helping pain is teething rings that you can put in the freezer, binky will help soothe pain too and when they get older and really start teething and it becomes unbearable for them the little remedies brand works very well for pain and is safe under a doctors guidance for the right dosage. 

My oldest had 2 teeth at 4 months. It's possible that the teeth are moving around and causing some pain. Try giving chilled wet wash cloths to suck on, or any teething toy and distraction works great too.