AC system no longer working.

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Hi, last year my front AC was fine but rear AC will come on only after 5-10 minutes of driving; This year however, the rear AC never came on and the front AC was working on and off - it blows cold for a few minutes and then blows hot air. I thought it needed refill, but it took one can R134a and only worked for 10 minutes. So I tried to fill more but it won't take. I had it checked in a shop and was told the A/C compressor is fine but they don't know why it's not blowing cold. Any help please? Thanks. As a single female, everytme I take my car to a shop for one thing, always come out with a long "needed done now" list. And the best part is, within the same day, my "list" changes from shop to shop. So I am in hope to learn more before I go. Thanks again!