Hi There .....can A Women Who Had Sex In Mid

hi there .....can a women who had sex in mid December and had period at the end of December become pregnant in January without any sex in January... also she has a ovarian cyst. during test for cyst she was given pregnancy test and it was positive. can she really be pregnant or due to cyst..it was protected sex in December....this women doe not wana do test infront of the partner. please advise...