I have a small skin tag near my right underarm. It’s not hideous or terribly noticeable, but I am a bit self-conscious about it, especially when wearing a swimsuit.

I had read on several health related websites that it was safe to remove it by tying a piece of string or dental floss tightly around it in order to cut off the blood supply and that in a few days, it would dry up and fall off. I tied a piece of floss around it yesterday morning, and now it looks swollen and is a reddish-purplish color. Is this normal, and how long will it take it to fall off? Also, when I changed the bandage I’d placed over it so that my bra strap wouldn’t irritate it, I noticed that there was a teeny tiny amount of “leakage” on the band-aid. I’m not certain this was caused by tying the floss around it though. Sometimes it would bleed a little bit if my clothing or bra strap irritated it. Should I be concerned about this? Has anyone else tried this method of removal, and what should I expect?
Yeah, I also read that it was safe to clip them off if you were very careful about sterilization. But, I chickened out! Figured the dental floss might be less painful.
Update in case anyone cares:

It had swollen to about twice its normal size, but today it shrank significantly and turned a very dark purple. It looks like it’s shriveling, so it shouldn’t be too much longer before it falls off.