It is very possible he just wants snuggles (not saying that's what he does want, just that it would be very common and totally normal at 3 months). I loved it that my boys would often begin the night not in my bed, but I usually brought them into bed with me at the first feeding of the night. They would wake to nurse, and I would lay them down next to me, latch them on, go back to sleep and that's where they would remain for the rest of the night. They got their snuggles, I got to go back to sleep (yea!) and if they needed to eat again, I was already right there.
Did your ped recommend you give your little one cereal? I know lots of moms swear it will help them sleep at night, but research in the last 10 years or so has shown that it's usually better for their tummies if you wait until 6 months (?) before giving them any solid foods, including rice cereal. Not trying to be critical. It's very possible you have a very good reason for doing so (reflux or swallowing issues). But if you were only giving it to him to help him sleep, I would consider trying to go without. The cereal could be upsetting is little tummy.
Good luck! Sleep deprivation is one of the hardest parts about parenting, especially with the newborns!