In addition to what Scott said (which is the first thing to do) it is possible (probable?) that you actually have already gone over your limit.
Dreamhost only “updates” the quota reports once a day, so if you received any significant amount of mail since the 96% usage report, you may have gone over quota (which will also account for the message).
One thing you can do is to go into the panel and raise the limit for that user. After this is recognized by the system, you should then be able to process your webmail. You can always go back into the panel and re-set your limits to the previous (lower) setting later, once you have decreased the contents of your mail box.