How to get around multiple file server caching?

Looks like I was moved onto the new servers today. I have a private server and now it appears I’m tied to three file servers as well.

My problem is, I’m designing sites and I’m uploading files via FTP and not seeing my changes because my browser is tied to one file server and the files I just uploaded went to one of the other file servers. (or so I think is happening)

Is there any way to control which file server I’m viewing via the browser so I can avoid this issue and see my changes? The pages I’m working with cannot be tweaked off-line since they’re using third-party commenting systems. Kinda stuck.