If you are hoping you are pregnant already, the Dollar Store and Dollar General have good, inexpensive home tests that you could take.
There are apps you can use to help you monitor your cycles, when it's safer to have sex, ovulation, any symptoms etc.. There are some that can also factor in birth control medications or past side effects. I use a basic period tracker that's free. As for your question about the depo shots, each person is different. Some people can get pregnant right after stopping while others can take months to years. There is no clean cut answer to that.
Given that you were recently on the depo shot it may be really hard to determine when you were ovulating and if it was while you had sex. If you do not start soon, your Dr. can do a blood test to determine pregnancy. If you do start soon just use an app to track it. Really makes life so much easier. Good luck
I think it is really hard to predict ovulation even WITH the ovulation predictor kits. I had a hard time with those. You should start tracking your cycle On average, women that have a typical cycle length, they can star having sex EVERY OTHER day on day 10 of their cycle (cycle day one is the first day of their period) and keep doing that until day 20. That usually catches the egg. Women ovulate around day 14 to 15 on average. Since you just came off depo, this is hard to predict for you. Likely, you will need to wait until you get your first period and go from there. And being late after coming off is common. You can take a test 2.5 weeks after you had unprotected sex to get an accurate result.