My front teeth are sensitive and the gums are tiny bit swillen on the inner side. Rotted tooth? Maybe tar build up? Gingevitis? Needs a cleaning?

Gingivitis. This sounds like gingivitis, or maybe early periodontal disease. Schedule a teeth cleaning, and discuss these concerns with your dentist. In the meantime, maintain good oral hygiene by brushing your teeth twice daily and flossing once daily. It is important to maintain good oral health, because it can affect your overall health as well.
See a dentist. A dentist will be able to diagnose the condition and make proper treatment recommendations related to the front tooth sensitivity and swollen gums. Pending the results of the comprehensive clinical and radiographic examination a dental cleaning and/or restoration may be warranted to help eliminate or reduce the disease and associated symptoms.
Multiple description. Cant answer your putting to much and no focus in what you want to know.