I have a mild case of pericoronitis and DO NOT have dental insurance and so far havent been able to find a free dental service In my area. Can I use do?

Community health. See if you can locate a community health center that offers dental services. Sometimes pericoronitis responds well to careful oral hygiene but not always. Contact HHS as suggested or your state health department. There are quite a few programs to help but they can be tricky to find.
Assistance program. Pericoronitis will not go away on its own, so it's important to see a dentist. Assistance programs vary from state to state. Contact U.S. Department of Health and Human Services to find out about care in your area. Another possible source of lower-cost dental care is a dental school clinic (low cost). Take care.
Other options. Only a fraction of people have dental insurance through their employer. And there's always a deductible, too, as well as a co-pay, so it's never free. You can seek reduced fee care at a dental school or hospital residency program. Healthcare financing is always an alternative. One way or another, you need to budget healthcare costs into your expenses. All the best...
Unfortunately. Unfortunately, small problems often become larger ones, whether it is medical, dental, auto, etc. It is always more cost effective and smarter to find a way to address these issues sooner rather than later. I'm sure you can find some way to work this out, both now and in the future. One cannot expect to get free care or services. Look for a job with dental coverage. http://www.freedentalcare.us/
Pericoronotis. keep the area as clean as possible. Rinse with warm salt water. Use ibuprophen for pain, 600 mg every 6 hours. See a dentist ASAP as this can get worse. You can see a dentist even without dental insurance. If you have a dental school or training hospital they may have low cost treatment programs.
Check dental society. Check in phone book or online for the state dental association or local dental society and research if there is a dental office that may help.
Seek dental school. Pericoronitis treatment generally involves antibiotic treatment to lower the inflammation followed by removal of the affected tooth. However in some instances pericoronitis is a stage during an eruption of a tooth which might not have to be extracted once eruption is completed. Your financial situation might be resolved if you find a local or nearby dental school with an oral surgery clinic.
Keep area clean. Pericornitis is swelling of the gums up onto the chewing surface of the tooth. It is caused by bacteria and most often occurs on the back side of the last lower tooth. This gum swelling hurts and is even worse if the opposing tooth bites down on these gums. The key is to keep this area clean until you can see a dentist-floss this area, clean with water pik, and do warm salt water rinses.
Insurance. Most people lido not have Dental Insurance, and if they do it often only covers a portion of the expense of treatment (copays, deductibles, etc.). Dental health care has to be budgeted for, just like internet access, smart-phone purchase costs, etc. Talk to Dentist about payment plans. Contact Social Services. Ask local Dental Society for sources. Good luck.
WaterPik. flush it regularly with an oral irrigator. Use a diluted non-alcohol mouthwash solution.