You can continue your medical treatment in Granada as long as you bring all the necessary documentation. However, we at Beststepsabroad would like to make an important recommendation. Please, inform your doctor that you are going to study abroad once the program accepts you. Just in case you need to contact him overseas.
If you are taking medication, maybe you could ask your doctor to provide you with enough for the whole time you are abroad. Sometimes, medical treatment cannot be given in full and students CANNOT get the same medication in Spain. It is illegal to deliver medication overseas.