Is it obligatory to make up the prayers that were performed while there was a spot suspected of being urine, without washing it, and if so, how does one make up the prayers without knowing their number?

You are not required to make up the prayers you performed while in that state. Either you were suffering from waswas (definition) (obsessive whispering/doubts) and Allah has now cured you, and one who suffers from waswas is not required to make up prayers. Or, you were praying while your clothes or body had urine on them, and you only became certain of this recently. In this case, your ruling is that of someone who prayed with impurity unknowingly. The preponderant opinion is that the prayer of one who prays with impurity, being ignorant of it or having forgotten it, is valid.