I would call the t and say that I am really looking forward to the May 3rd appt. but that I really need something a bit sooner. Would she please be able to notify you if there are any cancelations by other clients?
I know when I called a new t and I was thinking, Ohmygod how am I gonna hold out until then, so right then and there on the phone I said, 'oh that's an awfully long time to wait, I hate to come across so desperate but is there any chance we could meet sooner? I may be able to shift my schedule around to accommodate an earlier appt. ' And I was indeed offered an earlier appt.!
So I think you have nothing to lose by asking. If she still doesn't have availability sooner than May 3rd I'd ask her for a temporary referral. I'd be honest about my need for support and hope that she can at least empathise with you on that.
Take gentle care,