You do not have to recheck bags. They should be checked all of the way to SXM. Verify this on your luggage tags.

I would not attempt a 35 minute connect time in CLT. AA is in terminals B, C, and D. While they're all connected, there is some distance involved. Your arrival gate may be in the same terminal as your departure gate, but the odds aren't in your favor. Any delay in your arrival may mean an impossible connection. Any delay in deplaning may mean an impossible connection.