I so understand where you are cpming from. I have 2 bubs that don't sleep. I don't have a magic wand to fix your sleep problems - I wish I could.
What worked for me at 3 months - a 3 months old needs to go back to sleep after about 2 - 3 hours of being awake otherwise they get overtired and then can't get to sleep. If possible get a blockout blind for his room and make it dark and cool as possible. Have a consistant sleep routine - same song, same phrase "it's time to sleep now Mummy loves you" feed your little man in his room, pop him in the cot and pat gently until he falls asleep - it might take a while but it will work. he will soon associate the feed, the song and the sleeptime phrase with actual sleep.
I know it's hard and it makes you think "why does everyone elses baby sleep", rest assured they don't. I'm still up with DD 2-3 times a night and she's almost 14 months old.
Hang in there, if you're interested there is a sleep consultant that will do phone consults - google Sleep and Settle. She helped us enormously I would reccommed her.

Hugs to you xx