You have got to do what needs to be done without too many worries. All babies go through this and moms everywhere at first will worry about every little thing. At first they worry about everything, but the longer you are a mom the easier it gets. When he is 18 you probably won't even remember this. Since it is his first tooth it will probably be the worst; he'll get used to the feeling of cutting teeth. Fear not this will only last a few days at most so use the swing when needed.
My kids are are in their 20's now, and back when they were babies their pediatricians recommended that we rub their gums in the eruption area with liquid Tylenol. It worked better than any of the other products. The dentist that I worked for also told moms to take an ice cube and rub it on the area or buy the freezable teething rings. I also used popsicles which they really enjoyed. Beware of the mess though. LOL