The real issue with strep is that sometimes the sore throat goes away, but the strep bacteria doesn't, and it can lead to infections elsewhere in the body. Plus, rheumatic fever is a potential complication of untreated strep throat, although it's rare in adults.
There are some doctors who are of the opinion that not treating strep throat is a reasonable option in otherwise healthy adults, but they are in the extreme minority. Most health professionals, even those who are learning to be conservative about antibiotic use, will strongly advocate treating a confirmed case of strep.
http://www.annals.org/content/134/6/506.full.pdf
First thing to do, if you do want to treat, would be to get it confirmed. There are viruses that can lead to a sore throat; that is the most common cause. It is more likely to be strep if you have fever, and if you have swollen glands, but no congestion or cough.
If you do decide not to treat, please educate yourself about potential complications, so that in the rare event something does crop up, you'll be prepared to recognize it.
I also hesitate to get antibiotics, because I have ulcerative colitis, and antibiotics send my gut into a tailspin. I once chose not to treat a strep throat, for that reason, but I knew I was taking a calculated risk.
