What is causing me to wet myself early in pregnancy?

Pressure on bladder. The growing baby inside you could be pressing on nerves associated with your bladder and causing you to have some incontinence. This is not uncommon unfortunately. You may need to use pads. Discuss with your OB though for continuity of care.
Hormone changes. The hormones of pregnancy relax smooth muscles like those at the urethra, the opening of the bladder. Decreasing caffeine may help. Doing kegel exercises which strengthen the muscle will help both during pregnancy and to avoid problems afterwards.