Sorry to hear about all of your spam. Consider yourself lucky to only have 350 of these after a month. At my office address, which I don't even publish, I get almost that many every weekend!
Anyway, the best thing you can do is to delete them all. If your email client allows you to sort your inbox by subject, do so first. This will help to group the offending emails together. Then simply highlight all of them and delete them. DO NOT OPEN ANY OF THEM, if you haven't already. There are email tracking tools out there that report back that you've opened an email without you knowing that this is happening. That will ensure that your email address is flagged as a valid one, and you can count on getting more of this wonderful stuff in your inbox. If you have opened any of these messages and you see a link to unsubscribe, don't click on it. Again, all you'd be doing is sending a signal that your email is a valid one.
Once you've gotten past the current batch of spam, try to turn on the junk filters in your email client. You don't say what client you use, so I can't tell you how to do this, but there should be information out there on the web, if you can't find it in the help screens. You can set rules in Outlook, for example, to automatically route messages that have certain words in the subject, or that are from people not on your contact list, to a different folder than your inbox, so that you don't see them.
Whatever you do, just remember that the messages are spam. Don't take them seriously, and if you see any that ask for personal information, don't give it out.
Don't worry about changing email addresses. My experience is that these things come in waves. However, if you need to publish your email address, for a newsgroup, for example, then sign up for another one (hotmail, yahoo, etc), and publish that address instead. The spam will start to fill up that one pretty quickly, and not your "serious" email inbox.
Hope these ideas help.
on(Outlook, Outlook Express re are a few things you can do.