You can't give us a lot to go on, to be sure; we have never heard or seen you play. Before you start thinking about new equipment. I would suggest you try playing once with your mouthpiece in a corner of your mouth, rather than in the center. If you get a better tone immediately, this means you form your embouchure in the center of your mouth with a lot of bad habits. Most often this means biting too hard on the reed. You can get a similar problem by having the mouthpiece in your mouth at the wrong angle, so that you are either constricting the reed too much on the rails, or in the heart.
Even if the first experiment still sounds like a duck, your oboish tone can still be due either to not breathing deeply and freely enough, or keeping your throat too constricted as you play. As you play in the middle of your range, imagine singing a note in the bottom of your singing range, freely and openly. See what that does for your tone. Also try a different reed. You didn't say which ones you are using. If you still can't improve the tone, have an experienced saxophonist play your horn/mouthpiece/reed combination. If they can produce a more pleasing tone, so can you, with time. If they sound like a duck too, then and only then should you consider changing equipment. If you want a more flutelike tone, you can get it with a Caravan mouthpiece and Vandoren blue box reeds. As long as a tech has verified your horn is in proper working order, there's no need to trade a Serie III for anything else. But Selmer C*'s aren't all alike, and yours could be among the worse ones.
For an excellent home-study guide to working on your tone, try David Liebmann's Complete Guide to Saxophone Sound Production. You can get it off Amazon for about $90. The DVD has a lot of helpful stuff. Good luck!