He could very well be teething - my daughter started cutting teeth at 4 months of age, and by 12 months, she had every single tooth except her back molars which came in at about 15 months of age. It was pretty rough, as she teethed and teethed for months with no end in sight - needless to say, childrens tylenol and orajel became our best friends!
All children teethe at a different rate, but generally, the teeth will come in in a pretty regular pattern - look for his two front, bottom teeth to come in first. Feel his gums with your fingers and see if you can feel the little teeth beneath the surface (you may also be able to see what look like little white areas on his gums where the teeth are getting ready to push through) - my daughter loved having her gums "massaged" during teething. You will find that he may refuse the bottle/breast sometimes, so don't hesitate to use baby orajel to comfort him for a period so that he can feed comfortably. My daughter loved to chew on a soft, baby toothbrush: I also put those soft rubber baby spoons, her binkys, and wet washcloths/chew rags in the freezer and then let her chew on them.
However, realize that it is unreasonable for you to expect your 3 1/2 month old to "entertain" himself - he will now be looking for constant interaction and attention, and that is developmentally normal for his age. They don't care about toys at this point - they want to see faces, facial expressions, listen to voices, and interact with you. Teething is likely NOT the cause of his recent "inability" to entertain himself - now that he is sleeping less and become more aware of the world, he will not want to hang out by himself!