You have my complete sympathies - been there, done that.
A couple of things might be affecting your baby:
1. Babies are often born with their days and nights mixed up. This is because they were carried around by mum all day, and gently rocked to sleep in her womb. When night time comes, everything is still and they are often more active. I used to be kicked by my daughter before she was born from about 2-4am every night, cheeky monkey. Sure enough, when she was born, she was almost always awake around this time.
2. Is baby falling asleep whilst feeding? Babies sleep generally in 45min-1hr sleep cycles. If he goes to sleep sucking (breast or bottle) then comes into a light sleep phase one hour later, he may be looking for that comfort again to put himself back to sleep. Wherever possible, put him to sleep in his cot tired but awake. He will learn to put himself to sleep.
3. At 2.5 weeks, babies feed frequently. Breast fed babies especially need feeding every 2-3 hours, sometimes more frequently. It is helpful for the parents if feeding frenzies happen during the day, but unfortunately babies aren't very respectful of our sleeping habits.
Your baby is still very young. Anything he does now is not a sign that it will be like that forever.
You can try differentiating between day and night sleeps. For example, day sleeps in a light room, lots of household noise, etc. For night time start a relaxing routine of bath, feed, bed in a dark room.
During the day, feed baby upon wakening, have a short play (at 2.5 weeks a short play might be just 15 mins), then off to bed. This feed-play-sleep routine puts some structure in the day and your baby will eventually come to know what to expect. At 2.5 weeks there might be no playing between some feeds, which is fine.
At night, give minimal interaction - feed with as little light as possible (eg. a night light or reading lamp). No playing, just a quick nappy change if needed then back to bed.
Of course at 2.5 weeks, if your baby is distressed, comfort him. This might mean a firm pat on the bottom to calm him down. It might mean a pick up and cuddle. He doesn't yet know how to put himself to sleep, it is a learned skill.
To help you cope, take turns attending to the baby. If mum is b/f, dad can bring baby into her and then settle the baby back to sleep. Sleep whilst baby sleeps, including during the day.
Here are some references, which may be of help:
http://www.swsahs.nsw.gov.au/karitane/docs/survival.asp
The sleep and settling strategies for birth to 4 months might help you.
Good luck and be assured that your baby is very normal.