All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The blood you had after the speculum is not menses if a trustworthy doctor informed you that it is because of the speculum, unless it has the same characteristics of menses, or that it coincides with your menses, in which case it would be menses.
Therefore, if this blood is not menses, but bleeding because of the speculum, then you are obliged to perform the prayer and make up for the prayers you missed. However, if it was menses, you are not obliged to perform the prayer until you become pure, and you do not have to make up for the prayers you missed.
Allaah Knows best.