Hi Yuki,
So sorry to hear about your partner. I hope if he has decided to receive treatment that it was successful and you are both doing well. If not, there is no need to worry about you "catching" it from him. Prostate cancer is not the same as a cold or STD. Because cancer isn't a bacterial or viral infection, it does not spread between two people. Your own body can develop cancer, but he will not give it to you.