Is it worth saving up for a dive computer?
As has been implied in the various other responses, having a dive computer won't necessarily make you a better diver, but it will make you a more informed diver. A lot of us "more seasoned" (older) divers learned and initially dove without computers, and probably still could/would dive without them, but they have become almost standard equipment these days, to the point that some dive ops I have used will issue a computer to those divers who don't have one.
I dive a Suunto Cobra, which, arguably, is one of the more conservative dive computers in market, but I like it (but others don't). I'd suggest you do some research (even look for similar threads on this message Board) into the various types of computers (do you want a console or a wrist-mount, for example?) available, and their respective reputations and capabilities, and then purchase once you are satisfied that the one you have your eye on is most appropriate for the type of diving you are going to be doing.
This will be a major investment, and if you are into diving for the long haul, you need to choose wisely.
Good Luck, and many here are always ready to help with their opinions.