Is it possible for an egg to take 3 weeks to implant???!!?

If it was implantation then it would not have been from 21 days ago. At the maximum the zygote will implant in 14 day, usually 6-10. It could be implantation but if it is you had your ovulation day wrong or were stressing too much and delayed ovulation for a few weeks which is very possible. Take a test in a week to see and relax, you could cause a miscarriage if you don't. Good luck, happy baby making, and congratulations!!!!