I have a nasty cyst... on my fingernail bed... my nail came off partially and now... what seems to be flesh is starting to swell up and stick out.

Nasty cyst: This is called a "Mucoid cyst." It is really coming from the terminal finger joint below. Surgical removal usually fails because the trouble is in the arthritic joint below. There are worse things in life to live with. Medicine is not static so check back with an orthopedist, especially a hand surgeon in a few years. Meanwhile, try acrylic nails from time to time.