Oh my goodness, I went through an extraction that broke off when it was being pulled. Went through horrible pain as he dug out what I thought was all of it. Little did I know at that time there were several ... many ... little pieces of tooth all through. I got the tooth pulled in January, this is May, and I'm still not recovered. I refuse to go back to that dentist and can't find another to accept my insurance. I've had infection that I fought off with much persistence and much pain so PLEASE get back if you haven't. I'd be willing to bet that what you're feeling is pieces of tooth.
You should contact your dentist to find out what's going on. Normally the first few days are the worse and it gradually gets better over time.
Is there any swelling, fever, bad taste or any other signs on infection?