Chlorphenamine is a very satisfactory anxiolytic drug. The reason it is not commonly prescribed as a treatment for anxiety is purely commercial - the patents have lapsed, so it is not profitable for drug companies to market the drug to doctors, unlike the extremely lucrative new SSRIs.
Chlorphenamine is a very safe drug. Many patients have used it daily for decades in the treatment of allergies, with no ill effects. It's a far safer choice than alcohol. There are some contra-indications and side effects, so like any drug you should read the patient information leaflet carefully.
You may also wish to try promethazine, a very similar drug with stronger psychoactive effects. It is available over the counter as Avozine, a travel sickness remedy. Side effects are more common with promethazine, so I'd recommend trying chlorphenamine first.
If you're buying chlorphenamine from your local pharmacy, ask specifically for the generic version, which is far cheaper than branded Piriton. You can buy it very cheaply online (69p for 28 tablets from the link below). In either case, just say that you're taking it for hayfever and have taken the medicine before. Bear in mind that the recommended dose is up to 6 tablets per 24 hours, so you might want to stock up. Don't worry about looking suspicious, it's perfectly normal for people to buy several packets at a time.
Propranolol will suppress some of the physical symptoms of anxiety (rapid heartbeat, sweaty palms etc), but there's very little evidence that it improves the anxiety itself. It's generally most useful for people who are highly anxious about a specific event, like public speaking. It can also be useful in some patients for the treatment of panic attacks, by blocking the symptoms that spark the negative cycle of panic. People with chronic anxiety tend to get fairly minimal benefit from propranolol.
