Even if the serial number is not on the sleeve, it can usually be found on the round label on the vinyl record. I don't know of any truly great online catalogs, but sites like
discogs.com (which I like very much) lists release serial numbers in searches in a way that makes it relatively easy. Since it doesn't contain everything, it might not have your release entered into it though.
edit :
I suspect very serious collectors buy catalogs made for collectors or published by record labels (f.ex on ebay). As far as I know, record labels will only include vinyls that are in print in their catalogs, so you'd need a catalog from them from the time your vinyl was in production.