2 days after having 2 adjoining teeth temoved I feel as if some pointy pieces are still stuck in the hole. Is this possible or just my imagination? If there is some pieces still stuck without a root, would they come out by themselves?

The dentist should have shown you the teeth once they were extracted so you could see that the root tips were present or at least have informed you if they broke.

Sometimes there can be tiny bone chips that will eventually work their way to the surface.

You should call your dentist and tell him/her what you are feeling but DO NOT go poking around in the sockets!