Can the time of ovulation change drastically over a few months?

Yes it is possible because you won't always ovulate at the same time. Sperm can also live in your body for up to 72 hours. If your period lasts about 7 days then you add the 4 days after your period ended plus the three days the sperm can live inside your body then you get 14 days. This might not be an exact of what happened, but it's an example. Since you did get a faint plus sign then you most likely are pregnant. Reason being is because it is very rare to get a false positive. To make sure it is right, you should take a test in the morning when you first have to go to the bathroom because it is most accurate at that time.