Test positive for pregnancy only after missed period 1week is it possible?

Hi , can someone help me to count? my last period was 15-18dec, in Jan I missed my period so when to test but turn out to be negative for a week. 1. Is it possible to get pregnant and still can't test when u miss ur period for a week? 2.On 22nd Jan I got a feeling I'm ovulating so when to test for ovulation n it turn out to be positive...after 10-11days I test faint line with pregnancy kit. I have irregular menses so I can't count actually when I'm conceive can anyone help me. I believe is from the 22nd feb cos now is just a faint line not very dark line.