Should I stay on top of this medical malpractice?

There are two issues here:
1) Was this negligent, or unreasonably careless? The fact that you and your father both asked about antibiotics is not relevant, since you are (presumably) not doctors or other medical professionals; you therefore lack the knowledge or training to know when or when not antibiotics are appropriate. The issue is whether, given recommended or standard procedures for after a root canal as well as how your particular root canal went, the average reasonable doctor/dentist would have prescribed antibiotics. If under current generally accepted standards if care, you should have been given antibiotics, this was likely malpractice; but if under those accepted standards of care, a reasonable dentist would not have given you antibiotics, then they did nothing wrong--the complied with the accepted standards. In that latter case, there would be no liability. So it's not just that you had an unfortunate result; it's whether the dentist did anything wrong by current standards.
2) In a malpractice case, you can only recover compensation for your out-of-pocket (not paid by insurance or Medicare/caid) medical bills, lost wages from missed work (if any), and, for injuries or illnesses which caused significant, long-term (months or longer) disability or life impairment, some amount for "pain and suffering." (Or rather: unless the impact was signficant and long-lasting, while you might technically be able to get pain and suffering, the amount would be de minimis or trivial.) So if, as we hope, you had a short stay, made a full recover, and had modest out of pocket bills, there is little or no point in suing--you could spend more on a lawsuit than you would get back. In this case, there really is nothing to do.
But if you did incur large bills or some long-lasting life impairment, then consult with a medical malpractice attorney to see if you have a worthwhile, viable case. Many such lawyers will provide a free initial consultation to evaluate a case; you can confirm that they do so before making an appointment.