You are prescribed the medications for acne
after clinical examination, so I think you may go ahead with them. The only change I may make is that you skip tufacne and take the rest as advised. Yes tufacne may cause hair fall
but its not because of the side effects only that I am advising to skip it but also because if yours is not a very resistant form of acne then it should be cured with clinoxid , azimac and the rest of the medications.
Also see that you are properly hydrated with plenty of fluids.
Do not use any cosmetic products.
Use Lactocalamine lotion when you go out . It is both skin protective (sun block) and skin soothing