Air conditioner is not working

I had it recharged with dye after noticing the air conditioner was not cooling, although the fan and compressor were working. That coolant leaked out within five days. The mechanic looked at it and said the coolant was leaking out at the compressor. He pointed it out, but I could not see any evidence of a leak there. He said that the compressor needed to be replaced, even though it had still been going on and off as it was supposed to do. I have reason to believe this person may have been trying to take advantage of me.
Can anyone tell me if that really is necessary or is it possible to just to repair the actual leak and tubes leading to that point?
Since this car is seventeen years old and has other issues that need repair, I need to know the best and least expensive way to get the air conditioner going (and have it last a reasonable amount of time). I am a disabled senior and in Texas where it is already hotter than blazes. Can anyone tell me the best way to go about this and make my car usable this summer?