Here are pictures of skin conditions, including skin tags, moles and warts:
From your brief description alone, is sounds like a skin tag. Here are the differences:
1. Skin tags (slide #11 at above link): small flap of flesh-colored (or slightly darker) skin that hangs by a stalk. Not painful. It can be caused by other skin or clothing rubbing on the area. They can go away on their own, or a doctor can remove it.
2. Moles (slide #14 at above link): usually brown or black. Moles should be checked out by a doctor if they are painful, itchy, bleed, have irregular border or color, if they change over time
3. Warts (slide #18 at above link): Not painful, and many go away on their own. Most warts are caused from skin-to-skin contact and are a strain of HPV. There are some over-the-counter remedies to remove them (you can ask a Pharmacist).
I have had skin tags before, and if your bump is flesh-colored, it is most likely not a mole. If it is "hanging", as you said you could cut it off, then it sounds like it might be a flap of skin hanging from a stalk which is a skin tag. The location is also important, as you mentioned your clothing is rubbing in that spot. My skin tags went away on their own.
You could also have a pimple, but it does not sound like you believe it is this?
Watch the bump over time, and as long as it is not painful, no oozing (unless it is a pimple, and that would go away after a day or two), it is not uneven color, then you can do a "watchful waiting" to see if there are any changes. If not, it is most likely one of the skin conditions above and is most likely not harmful. Bottom line: when to have a doctor look at it: change in color, uneven color, pain or discharge.
I hope this helps!