"I do not know your university schedule."
Translation:Senin üniversite programını bilmiyorum.
You can only have one possessive suffix on a word at a time. Ergo, if you have a possessive pronoun before something, you no longer have to form a noun compound (which is just a form of the possessive suffix). Basically. "Senin üniversite programın" + "ı" = the phrase
And you were right about "programınızı"