Hi,
I wouldn't recommend having caffeine on propranolol (or in general). The idea of you taking this is to reduce your anxiety, however caffeine will actually make you feel more anxious and so you might not feel the benefits of the propranolol if it is having to try and counteract not only your baseline anxiety levels (which I gather are quite high) but also the added effect of caffeine.
In my personal experiences, when I'm feeling anxious I avoid caffeine all-together as I know that it tends to elevate it and makes me feel worse. I have taken beta-blockers before, however I never took them with caffeine, so in that sense I can't give you my experiences on it.
This is just my view, but if anyone is more informed then feel free to correct anything I've written.