Hm, this is always tricky. And even under the best of circumstances, it's an educated guess. Sperm can live for a few days and we ovulate at different times even when we are generally regular with our cycle. Day one of your cycle is the first day of your period. So, you had sex on day 6 of your cycle. Greater fertility generally starts on day 9 for the average woman. But . . . you never know. You could have gotten pregnant then or any of the other days. Are you trying to determine paternity?
Did you get an ultrasound in early pregnancy?
You ask if it is possible you got pregnant the day after your period. Sure, it is. But you wouldn't have to -- in a way you are asking the wrong question. This is because sex on the 29th would produce sperm that lasts up to 5 or 6 days in your body. (Sperm has a long lifespan in the woman's reproductive system.)
This would mean that you could get pregnant from the sex on 5/29 up until probably 6/3 or even 6/4. (Incidentally, when you "squeeze out" semen, you are not getting rid of the sperm, they are fast little swimmers and were probably halfway up your Fallopian tubes by then. The semen is just the bus, the sperm are the passengers and rushed off the moment it hit your vagina.)
You say your cycles are always 28 days, but you had just been on Nuvaring, right? If your body unaffected by Nuvaring naturally had 28-day cycles so accurately that you could set your watch by it for years and years and this had all happened at a time when you had no influence of Nuvaring, then one could say you would be expected to ovulate on 6/6. But unfortunately, you were just off Nuvaring, and cycles can take a while to adjust when you are out of its influence. Women complain all the time that their cycles are totally out of whack for a couple of months when they adjust their birth control, or go off it.
Did you have an ultrasound in early pregnancy? And based on it, did they give you an estimated due date? If it was early enough, and if they used only the ultrasound to determine the due date (and didn't use your reported first day of your last period), you might be able to tell from that information when you conceived. If you didn't have an ultrasound in the early weeks, though, you probably won't have information useful enough to be able to rule out either guy until you have a DNA test.