Is it permissible for me to wait until the fifteenth day to consider it the end of my period and purify myself, knowing that I am on the fourteenth day and do not know if I have become pure due to IUD bleeding, and am I sinful for doing so?

The maximum duration of lochia (postpartum bleeding) is forty days. Therefore, whatever you see before that is considered lochia. What extends beyond this period is not considered lochia or menstruation, unless it coincides with the time of your regular menstrual period, in which case it is considered menstruation. Otherwise, it is istihada (irregular bleeding), and you should do what a woman experiencing istihada does: perform ablution for each prayer after taking precautions (e.g., using a pad), and pray as many obligatory and supererogatory prayers as you wish. You have all the rulings of ritually pure women. Some scholars hold the view that the maximum duration of lochia is sixty days, and according to this view, you would still be in a state of lochia.