Hey pandagirl97,
Late or missed periods, for reasons other than pregnancy, are quite common! Bodies are quirky, and so most menstruating people will occasionally have a period that's earlier or later than usual, or even skipped altogether.
Missed periods are associated with hormonal IUDs (such as Mirena or Skyla) rather than copper IUDs (which don't have any localized hormones). So your missed period likely is not related to your IUD. This article,
M.I.A or, Dude, Where's My Period?, explains some common reasons for missed periods. The article ends with a few next steps with a late period--Take a pregnancy test (You did that! Also IUDs are over 99% effective in a year of typical use, so pregnancy is not likely). See your healthcare provider (if you have missed two periods). And try not to stress! "You're in good company: thousands of periods go missing in action every month, and most of them turn up in their own sweet time."
I also want to follow up on the "really bad pains" you are experiencing in your abdomen. The copper IUD is known to worsen period cramping in some people, so it is likely that is what's going on. How do these abdomen pains compare to your period cramping before getting the IUD and in the 3 months since getting it? And have you found anything that offers relief from the pain?