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I got my first card in mid March. My first FICO was 6mo later, in September. I think yours will be May, not April.
You can get a free EX FICO from Discover at www.CreditScoreCard.com
Definitely don't pay for anything that costs a lot until you're sure that you have a score. As mentioned, Discover is free. You can that out soon after April 1. Or you can grab a $1 trial at CreditCheck Total and cancel during the trial period.
Has your lender said that a score is necessary? You'd have reports right now; they simply wouldn't generate FICO scores. Maybe it's possible that what's on your report right now would be sufficient for a loan despite the fact that there isn't a score yet.