If so you need to get a serious move on. The quoted time for the identity verification for the FAA is 90 days! When I did it, it only took a month, but you're cutting it a bit fine for May.
You need to fill in this form and fax it to the FAA:
http://www.faa.gov/licenses_certific..._verification/
And fill this form in and send it to the CAA so they'll release your info to the FAA:
http://www.caa.co.uk/docs/33/FORSRG1160.pdf
(they charge you about £40 for the privilege)
When they've nattered to each other the FAA send you a letter. Make an appointment at a convenient FAA FSDO, and show up with your passport, JAA license, medical, logbook and the letter from the FAA. They'll then issue you with a temporary airmens certificate on the spot. They won't charge you for this. Once you've then completed a BFR, you're all legal. The proper license should arrive in the post in a couple of months.