No, there won't be any problem in doing so. If you done your 10th Std in one state then as per the rules you can pursue your PUC from any other state without any problem. You will have to struck off your name from the previous school and do a fresh registration / admission into the school of your choice in Telangana. However, when taking admission into the school, they will guide you with all the necessary formalities to be completed.

Hope it helps.