Dear Kristina,
A mistake many parents make is to take the child out of the crib too soon, and you did this. It generally results in problems. But, now that your son is out of his crib, you will have to be resolute in having him sleep in his own room/bed. Some children do prefer sleeping on the floor, and you can make a comfortable arrangement for this, chiefly by using a mattress on the floor, without the bed. One way or the other, the key will be setting firm and unyielding limits on his coming to you - only you can see to this. At this point, I wouldn't put money into purchasing a new bed. That can come later when your son has become more comfortable sleeping in his own room.
At least he sleeps by himself. My 6 yr old is afraid of having nightmares and won't sleep by himself. We even let him pick out new bunk beds, a night light he liked, a TV for his room but no go. I still have to sleep with him. So count your blessings.