A beta-blocker such as propranolol should ease the epinephrine, aka adrenaline, surge and associated increased heart and respiration rates of the flight-or-fight response, however, they don't directly affect anxiety and there are better treatment options, imo.
Anxiety disorders (also depression) are the emotional symptoms of a brain dysfunction,
atrophy of the two hippocampal regions of the brain caused by high brain stress hormone levels, mostly cortisol, killing hippocampal brain cells and inhibiting the growth of new ones. It is arguably an auto-immune reaction. Both
antidepressants and the cognitive, behavioural (CBT, REBT) and mindfulness
therapies stimulate the growth of new hippocampal neurons. It is these new neurons and the connections they form which produce the therapeutic response.
For a more direct effect than that of propranalol, you could try the prescription antihistamine hydroxyzine which has fairly good anti anxiety properties (hydroxyzine comes in two forms, hydroxyzine
pamoate (Vistaril) and hydroxyzine
hydrochloride (Atarax). Anecdotally, the pamoate form is claimed to be the more effective for anxiety). Benzodiazepines such as diazepam (Valium) should be avoided as they can have the same affect on hippocampal neurons as cortisol (as does alcohol and the THC in cannabis, btw).
However, imo, antidepressants and/or therapy are the better treatment options.
Both propranolol and hydroxyzine can be sedating and propranolol may reduce the heart rate and impact physical activity to some extent. Antidepressants may have more severe side-effects at the beginning although this is by no means a certainty as most have none to mild symptoms, but these can be mitigated by starting on a low dose and ramping it up by small increments over a few weeks to the recommended starting dose.
The important thing is to get the anxiety under control as unrelieved stress has long-term impacts on health.