How to put a co-worker in their place that is trying to get me in trouble...please help!?

There is a long story behind this so i will try to keep it short. I work in a law firm and I was asked to back up a department for two months while her supervisor was out on sick leave. I was unfamiliar with the department so I needed to ask a lot of questions. This girl was on personal phone calls all the time and making me do most of the work and when I asked a question more than once she would get angry and tell me I was taking up her time and she couldnt get her work done. I tried to be as polite as i could and didnt want to go to my boss about her personal phone calls because i had to continue working with her and didnt want to cause more friction. The girl who was on sick leave is known to be just as imcompotent as a worker and as well as the girl I was working with and I think they thought I was going to permenantly replace one of them, meaning one of them would get fired. Every little mistake I made she went back and told my boss. The department was in the calendar department, which there is a lot of information to be retained and a lot of info to remember so god forbid if I should ask a question more than once. I had enough so I went to my boss, told him about her personal phone calls and about her not being willing to answer my questions. I was working my you know what off and just kept getting hell from her. I am now out of that department and back into my regular spot. She found a miskake I made months ago, brought it to my boss' attention rather t han just coming to me and either asking me nicely to fix it or just ignoring it. Over the past few months I found plenty of mistakes she made and I just corrected it myself and moved on rather than wasting company time by being a snitch and telling my boss or bringing to to her attention. Since she wants to play tit for tat, should I tell my boss every mistake she makes. Also, should I report her to the Human Resources department. I am a working mother and I support my husband who is laid off and my 8 month old son. My natural instict is to give her a wack...lol! I need to keep my cool and deal with her in a professional way and I want to get her in trouble in a slick way. Any tips? I know this sounds childish but you would need to be there to see what goes on. I am a hard worker go to work every day, dont make personal phone calls and am respectful when people need my assistance. Please advise. Also, what are some warning signs people are trying to get you fired?