There is a chance of getting pregnant anytime during the month. On a 28 day cycle, though, you're more likely to be ovulating on day 14. If I had to pick a day, i'd say go for a day or two after your period ends. It's not very likely that you've ovulated yet, and if by any chance a sperm or two slip out of the condom, they will likely be dead before you do ovulate. It's not fool-proof, but that's the best bet, I think.
Why won't your mom help you get birth control? Maybe you should sit down with her and let her know that you plan on having sex with or without, but that you would rather do it with, because you don't want a baby. Ask her which she would rather deal with: taking you to get birth control, or having a screaming infant in the house. I think she'll choose the first!!
Daile