It's possible, though the latter is extremely unlikely if you're only sending text messages, no links, images or anything else. And there's little you can do to protect yourself beyond not use high risk programs. A proxy server will not help and anyone who claims that will somehow increase your security is someone who has proven they know basically nothing about computer security.
Honestly, a far more credible threat is the amount of personal and potentially sensitive information Yahoo can collect on you through using their official client. That then gets sold off to third parties who will do who knows what with it. Facebook, Twitter, and all the rest are the same way. Someone with sufficient desire to do so, could learn a great deal about you and use that to make your life rather miserable.
I've heard that people can hack into both your Yahoo account AND computer through just chatting on Yahoo Messenger; is this true? What can I do to protect myself? Would using a proxy server help?