1995 Toyota Celica timing belt? Or not

I have an automatic 95 toyota celica. I was on the freeway and all of a sudden my car powers down. It sounded as if I dropped it in low. I pull over, car fully dies. I try to start it and it trys to start but doesnt fully start. I got a tow. I jumped it and nothing. About 45 minuted later it starts. I drive about half a mile and it just shut off while at a red light. Tryed to start it and it trys to start but once again failed. I had some friends try to mess wth it and then it started again. Was able to get it to my boyfriends house. But now it still wont start. We had a mechanic come look at it. He said he was pretty sure it was timing belt (he only checked by hearing the car since I didnt pay him) he didnt actually take anything apart. He thinks its the timing belt but some people are saying that if it is the timing belt it wouldnt have been able to start up again the way it did before I got it to the house. Any suggestions on what it is? I dont have any money to to be buying parts and testing different things.