Does having an aunt with uterine cancer make me more likely to have one too?

Possibly: There is an inheritence pattern for several cancer types, including ovarian cancer. However, knowing the specific type (endometrioid, serous, brenner, mucinous, etc), would make a definitive comment more meaningful.

Endometrial cancer: What you describe alone (one second degree relative) does not increase your risk. A complete family history as well full history and physical is needed to know your risks.