Jealous co-worker...what should I do?

I started working for my current employer a few months ago and have already received a promotion. Another co-worker got mad at me and told me that I hadn't "paid my dues". She started complaining about how it took her a year to get a promotion then started saying things like, "I bet you're going to get a pay raise now" (in a frustrated tone). Now, she's giving me the cold shoulder. Initially, I sympathized with her, but now, she's just starting to get on my nerves. More importantly, her mother also works at the company and is my superior. I feel like if I complain to her mother, I may end up burning bridges. I also feel like this girl could prevent me from advancing in the company. This girl throws a hissy fit whenever she doesn't get her way and constantly complains. I could complain about a lot of things, but I don't, and I really feel like i deserve this promotion. How do I make my sentiments known without hurting anybody's feelings?