Is there anything you can do when a professor discusses some of your personal concerns with other professors potentially mockingly?
I was going to vote to close because you're an undergraduate, but I checked the fine print and I think we're okay here -- this is a situation which could easily occur to a grad student.

If you still want to talk to the guy who canceled your appointment so rudely, I suppose you could visit his announced office hours and try pretending the whole thing didn't happen

However, if you don't mind being patient, the other approach would be to learn from this experience that your department is a gossip den, and be more circumspect in future; and trust that after some weeks or months, the good guys in your department will realize that you are a serious student worthy of helping.  This approach could be called taking the moral high ground and biding your time.