Propranolol - Is it OK to stop propranolol and start taking fluoxetine instead?

Hi, Naomi!
It's best to taper off propranolol if you've been on a high dose for a length of time and have been taking it for a cardiac disorder. If you're on a low dose for anxiety it's probably safe to stop especially if that's your doctor's recommendation.
Propranolol is used to help reduce the symptoms of anxiety (tremors, racing heartbeat, palpitations, sweating, etc.) but it doesn't address the underlying cause. Fluoxetine is more of a longer term medication to alleviate the anxiety itself.
It won't work immediately and it may take a couple of weeks before you start feeling improvements. It can take up to 6-8 weeks to feel the full effect of the drug but you'll be feeling much better by then.
Best regards,
Wildcat