I want to know whether or not I can sue over my medical problems that occurred earlier this year due to neglect?

Medical malpractice is negligence.  Negligence is the failure to exercise due care (that degree of care that in this case a reasonable nurse practitioner would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care mentioned above), breach of duty (failure to exercise due care by the nurse practitioner improperly inserting the IUD), actual cause, proximate cause, and damages.  Actual cause means but for the nurse practitioner inserting the IUD, would you have been injured?  If the answer is no, actual cause has been established.  Proximate cause means were there any unforeseeable, intervening events which would relieve the nurse practitioner of liability?  If the answer is no, proximate cause has been established.  Damages means the amount of compensation you are seeking in your lawsuit for negligence against the nurse practitioner.  Your damages would include the medical bills, pain and suffering and documentation of any wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  Compensation for pain and suffering is an amount in addition to the medical bills. The medical reports will be used to determine compensation for pain and suffering.

It would be advisable to obtain your medical records from the nurse practitioner and the hospital ER and the surgeon who treated you.  The medical records/medical reports from the hospital ER and the surgeon will document the nature and extent of your injury and will provide evidence of malpractice by the nurse practitioner if the nurse practitioner improperly inserted the IUD.

Prior to filing your lawsuit for negligence against the nurse practitioner, it may be possible to settle the case with the nurse practitioner's insurance carrier.  Your claim filed with the insurance carrier should include the medical bills, medical records/reports and documentation of any wage loss.  If the case is settled with the insurance company, NO lawsuit is filed.  If you are dissatisfied with settlement offers from the insurance company, reject the settlement offers and file your lawsuit for negligence against the nurse practitioner.  If the case is NOT settled with the insurance company, you will need to file your lawsuit against the nurse practitioner prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.