Is is proper to send a graduation announcement to a member of the same graduating class at a different school? Any advice would be helpful as I need to send my announcements in the next 2-3 weeks.

Of course you can send it to someone in the same class at a different school. You can send them to whomever you like. They might use your announcement as a keepsake for the time that both of you spent in school.

If you are saying that someone at a different school is also graduating this year, yes of course it is proper.

If you are saying that someone at a different school is part a multi school graduation ceremony that you both will be participating in together, then no. Athough it is not improper it is rather a waste of an announcement.

The only thing improper with sending out a graduation announcement is the expectation for everyone who has received one, either to attend and/or to give a gift.