My web designer made changes to my site and he told me it was changed. I saw them on my end, but when my friend opened my website in New York, he still saw an old page that was completely replaced on my FTP.

How are they still seeing that. Does my hosting provider have anything to do with that? (I have a cheap one) Or does it just take awhile...?

It's been 2 days.

So, there's only one person who saw this old page? Ask him to clear his browser cache.

I don't think so...It might be that your friend is viewing the cache by accident (happens to me ALOT with ie) and I have to like restart ie for it to 'refresh'.