Question regarding Ciplar LA (Proplanolol) usage and side effects?

Hi, I have been taking Ciplar LA 20 mg (Proplanolol Hydrochlrodie Long Acting tablets) for over 3 months now and it has been really useful in controlling my anxiety levels. The doctor told me that I can continue to take it throughout my life and that it will not have any problems. I have two questions:

a) If I continue to take 20 mg daily, is it that my body will become immune to 20 mg dose later on and then the 20mg will not have any effect? In other words, do I need to increase the dose after some time to see similar benefits or is it that I can continue with 20 mg and there will be no need to increase the dose, but still see the same benefits throughout my life?

b) Is this going to cause any side effects? I know that I am taking a very mild dose, but in-case I switch to 40 mg, is it going to show any obvious repercussions?

Thank you.
-Kumar