I shouldn't laugh... but I've been there and done that TWICE in 20 years. Once for over a week, the other I forget, but it was awhile. As in long enough I was having sex and neither of us noticed. Ewww ewww ewww, gross, icky, gross. I've also gotten fairly compulsive about "checking" at the end of each period now.
And if it makes you feel better, I know from working in a women's clinics LOTS (hundreds of women just from our clinic alone) have done this. (Made ME feel better at least). And talking with nurses (who notoriously have NO shame), most of them have done it at least once.
It happens. As long as you don't develop a fever, and the smell goes away over the next 48 hours, you'll be fine.
One of my sisters has a phrase I'm going to borrow:
"Nothing injured but my pride."