If you can remember enough of it you might try writing down a Parsons Code and searching against, say: https://www.musipedia.org/melodic_contour.html
There's also Midomi, into which I similarly whistled, hummed and even made some endeavors at singing, and likewise got no luck.
I feel like there indeed should be a music search engine that works from whistling, but I haven't encountered one so far.
In a vaguely topical sentiment, I several times had success with Audiotag.info—but you need a piece of the actual music there. It worked better for me than Shazam, SoundCloud or Picard. Probably because I'm unlikely to be looking for a hit song—now, ‘William Tell’ on a xylophone is closer to my thing: https://www.youtube.com/watch?v=gXajSUb29ZY (also related: https://www.youtube.com/watch?v=mRXUzWNdLx8&t=9m40s).