Just out of curiosity, which type of kava was it and where did you get it from?
I haven't had that from kava, but I have a lot of experience with allergies and systemic allergic reactions. Kavalactones ought to clear your system within 72 hours, but if you're anything like me your immune system could have problems returning to baseline even though the offending substance is no longer in your system. If you're taking any MAO inhibitors or other things that impact liver function, that could delay metabolism. I suggest drinking lots of fluids, maybe make some of it coconut water or something like Powerade so your electrolytes don't get too far out of whack. For a reaction like that, the non-drowsy meds like Claritin, Allegra and Zyrtec are not going to do shit. Benadryl is the best in that case if it doesn't make you too drowsy, second best is Chlortrimeton (or the generic Chlorpheniramine Maleate or HCl). I find that Chlorpheniramine is less likely to make me drowsy, but I am pretty well acclimated to antihistamines in general. Prince Phillip recommended Walhist from Walgreens, which is a generic form of Tavist, that's great stuff as well and works for 12 hours.
For the hives, I recommend Benadryl liquid or hydrocortisone, depending on how large of an area you need to apply--you don't want to cover too much of your body with hydrocortisone because you absorb it through the skin, Benadryl is safer to apply to a larger surface area. If it is all over your body, I recommend Sarna Sensitive lotion for covering everything, also the Aveeno products are very good (unless you are allergic to oats). Soaking in the tub with Aveeno bath or a cup of Magnesium Sulfate is good to get some general relief for the itching.
If it doesn't start to improve shortly, the best thing is probably to get a Medrol dose pack (Solumedrol, a prescription steroid) also Dexamethasone is good--I have major autoimmune problems and have had some reactions where that was the only thing that would stop it, but the relief was very rapid once I started on the Medrol. If the itching is really bad, Naltrexone helps if the doc will give you a prescription for that, normally that is used for opioid withdrawal, but it works. Hope this helps and that you are feeling better soon.