I have a skin tag that turned black an fell off is this dangerous?

No: This is very common. The "old fashioned" treatment of skin tags was to tie a small not around the tag and tie it tight. This would "choke" the tag. It would turn black and fall off. In some way, you gave yourself a similar treatment. There is actually a study comparing this method to a more modern "surgery" of the tag and it showed that the older string method had better cosmetic results.

Skin Tag: It's difficult to tell without examining you, but sometimes the blood supply to a skin tag can become cut off. The skin tag then dies and falls off in a process called autoamputation.