Can I sue a doctor in the Dominican Republic?

Hi. Yes, you can sue a PS here in Dominican Republic as in the US. Make sure your underwent surgery with an acreddited one. But be  aware that under the laws you should have signed a "Inform Consentment and a Contract for Surgery". The inform consentment explain you about all the complications, risks and unfortunate events that may occur in any plastic surgery procedure that are not under the  control of the medical science, the surgeon or the patient, not in DR nor in the whole world. 
 It is  stated by the "Health Law"  of  the Ministry of Health of the Dominican Republic that you should be informed of all of the possible complications and risks before opting for any elective procedure. So you should ask your surgeon for both documents and be sure it was an act of negligence and not one of the many possible events and complications statistically stablished by all Plastic Surgery Treaties,  and  informed to you before surgery.
International Member of the American Society of Plastic Surgeons (ASPS)
Member of the International Society of Aesthetic Plastic Surgery (ISAPS)
Member of the International Confedaration of Plastic, Reconstructive and Aesthetic Plastic Surgery (IPRAS)

I am sorry to hear about the complications you have experienced.  At this point, I would encourage you to focus on recovering from your surgical procedures and returning back to good health.  As you likely know,  focusing on good nutrition will be one of the keys. When the time is right, you will likely benefit from in person consultation with well experienced board-certified plastic surgeons in your area. Achieving an outcome that you will be pleased with long-term should be one of the goals. Eventually, once you have utilized your energy achieving an outcome that you will are pleased with, legal advice from experienced/ethical attorneys will address the question you pose here. Best wishes.