Did the doctor give you any explanation?

Some possible explanations that come to mind are:

1) The prostate is very swollen, closing down the urethra.  When
you build up a lot of pressure, a bit of urine can be forced through
but as soon as the pressure is relieved a bit, it closes off again.
So you never relieve much of the pressure and you always feel a
need to urinate.

If that's your problem, I would think the bladder would always feel
full.  You'd feel a need to urinate all the time but have trouble doing
it.

2) The bladder took some radiation hits.  It's irritated and burned,
like sunburn, but inside you.  Urine in the bladder irritates it further
and make you want to urinate to get rid of it.

With this one I think you'd feel a need to urinate frequently, and
have little trouble doing it, but it would only give you temporary
relief because as soon as a bit of urine collected in the bladder
you'd feel an urge to get rid of it again.

3) There's nothing too much wrong with you but the drugs are
causing you to have to urinate.

If the problem is number 3, it's real easy to solve.  Just stop
taking the drugs.

If the problem is 1 or 2, those things heal by themselves, but
they take a while.

I'm pretty sure I was suffering from problem number 1 after my
radiation treatment.  I felt a great urge to urinate all the time, but
had trouble doing it.  Flowmax fixed me up.  I tried to get off it
gradually, but it was difficult.  It took about 3 months before I
was healed up enough that I didn't need the Flowmax to make
it possible for me to urinate.

   Alan