Unless there is something more concrete than what is in your post, I don't see a serious problem. The difficulty seems to be based almost completely in your
perception of what the situation is.
In my opinion, if this person's making sarcastic comments to you is the extent of your difficulty with her, that's not really something you would take up with a supervisor. You may come across as whiny or unable to fend for yourself in the workplace.
If others are telling tales to you about this individual you should be very very careful what you believe and what you do in response to these tales. It's workplace suicide to get sucked into office politics and especially if there is a feud between two co-workers.
Do your best at your job and keep things business-like. If I were in your shoes and this person's comments affected the quality of my work or my reputation with others in the office, I would speak to this person one on one in a non-confrontational, business-like manner to resolve it.
If this person's comments are not affecting the quality of your work or your reputation in the workplace, I don't see a problem. You may need to develop a thicker skin
Good luck!