Can someone have both bpd and cyclothymia?

Yes: If bpd means bipolar disorder, then by definition there has been at least 1 episode of mania. The DX of cyclothymic disorder allows for hypomania, but not for a manic episode. That said, however, there may be times that bipolar disorder acts like cyclothymic disorder for periods of time.

Possible: I suppose it's possible but highly unlikely. A full psychiatric evaluation by a seasoned pro is indicated to help make that determination.