I think my wisdom is coming in and the gums around the secomd molar on the bottom right are very swollen and painful. No skin has broken, What is it?

You are right. You guessed right. It is inflammation due to pressure from your wisdom teeth on your gums. You should see a dentist or an oral surgeon for an evaluation. .
Oral Surgeon ASAP. See board certified oral & maxillofacial surgeon for exam/xrays/recommendations.
See your dentist. There are many reasons your gums around your second molars may be swollen. I am sure that your dentist can properly evaluate your condition, and treat this problem properly.
Wisdom teeth. Sometimes wisdom teeth are valuable asset when healthy and properly aligned, but more often, they are misaligned and require removal. The removal of wisdom teeth is one of the most common procedures at ages 15-24. See your dentist for evaluation and x-rays.
Could be. Could be wisdom tooth, but there are many other reasons for swelling. Please call your Dentist for an examination and for best treatment advice.
Wisdom Tooth ? You might be right. See your dentist to determine if that is the cause.