Is severe dental pain after incomplete extraction normal?

YES: See your dentist or an oral surgeon and complete the process and get healing started.

Extraction: I am not sure what you mean by an incomplete extraction. Some discomfort is to be expected after an extraction. If the pain increases after 3 or so days and it was a wisdom tooth it may be a dry socket. See your dentist for follow up.

Probably. : While i don't know the details of your situation, "incomplete" suggests this was a complex situation that may or may not involve (an) additional procedure(s) to close the loop. I recommend you see your oral surgeon asap to wrap things up and get started healing.

Root remaining?: An incomplete extraction could mean that part of the root or tooth is remaining. If a residual root that still has pulpal tissue (nerve inside the root) remaining, you could experience pain. If the procedure was a complex surgical procedure and a small piece of tooth was not removed for various reasons, the pain could be from the surgery itself and not from the residual root.

Probably: Need to get the root out, if it was left in. May depend on how long you have had the pain and severity.

Surgery: There will be pain after any surgery. Failure to complete the procedure, and the unsuccessful excessive tissue and bone manipulation, would only add to post-operative discomfort. Please see a specialist, an oral surgeon, for the least traumatic resolution of your problem...The remaining part of the tooth root has to be removed so as not to be a focus of infection.

Yes, but: Leaving an "incomplete" extraction unattended is not normal. If you were treated by a general dentist, they should have referred you to an oral surgeon for completion of treatment with in 24 hours. If seen by an oral surgeon they should have reappointed you for follow up care with in 24 hours. Please see a qualified oral surgeon asap in order to get your problem properly resolved.

Incomplete: 2 reasons for incomplete extraction. 1) Dentist couldn't extract whole tooth in difficult extraction or 2) oral surgeon left part of tooth by plan with 3rd molar root close to nerve. In either case, solution is to ask dentist for strong pain med and see oral surgeon ASAP.