Will I be able to attend school for medical billing and coding and get a job afterwards if I have a felony on my record?

Until the felony is off your record, no medical school will take you. You are a liability to the school and program especially if it was a drug felony.

One could argue if medical billing and coding is actually in the "medical field" but in general you will not be able to have access to medical records with a felony. I know in our medical supply company you can not have any patient contact with a criminal record ( felony)