Hi Itchy, you have my sympathies, it's an utterly horrible disease. I don't think it's taken seriously enough and is too easily dismissed. I had a couple of very similar episodes a few years ago, triggered by a flu-like virus that caused a massive immune flare up (crippling reactive arthritis, followed very swiftly by hives all over my body which stopped me from eating, sleeping, working. Truly awful.)
I had similar treatment as Itsmymess - mahoosive off-licence dose of fexofenadine (chemist never had enough in stock & even half a prescription filled a carrier bag!), montelukast & doxepin (which had the added side effect of sedation, which really helped me to sleep). I dialled back on the latter two and stayed on fex for a while. The combination was miraculous, and from memory it worked almost immediately - definitely nowhere near two weeks.
I only got access to those drugs via a private dermatologist - my GP was happy to refer me on the NHS but said it would be months before I got to see anyone. Once he'd prescribed and written to my GP all my prescriptions were on the NHS after that.
One thing I remember the dermatologist saying was that there are a gazillion antihistamines out there and if this combination didn't work then there were other options.
I would bang down the door of your doctors - you shouldn't have to suffer, and 2 weeks is long enough to know that your current dose isn't working.
NB my hives have never returned. They weren't triggered by stress, heat, medications etc and after two episodes after the virus, touch wood I've never had them again. Appreciate yours may have a different cause but the 'thunderclap' type (as my dermatologist called it - ie no previous history, came on hard) apparently tend to go away and not come back.