I don't know what type of music you're considering playing, but consider stepping outside of the piano/guitar realm. Trombone would be perhaps your best choice. A very difficult instrument to learn and master, but it requires only enough fingers to grip the instrument securely. (You could probably get away with a thumb and finger on each hand). The trombone can be used in any type of music; there are great trombonists that specialize in rock music, for example. Classical, jazz, new-age… the possibilities are endless.
Alternatively, if you are dedicated, consider specializing: if you learn to play pedal steel guitar (fewer finger requirements) and perhaps something like accordion, harmonica, etc., you could join a rock band with that skill-set fairly easily. Learn to sing, at least for backups, and you make yourself even more promising. (Again, I don't know what type of music you're looking at).
HOWEVER: Don't sell yourself short with only three fingers! Guitar would be tough, since the thumb can't do a whole lot, but with alternative tunings and a lot of practice, you can accomplish a lot. My father lost use of three of his fingers in a table-saw accident. He eventually regained full use of one of them, but had his middle finger amputated, and has no ability to bend his forefinger. (This is all on his left, fretting hand). He primarily plays bass in his bands now, as it's less frustrating for him, but hearing him on guitar, with the help of alternative tunings, it's difficult to tell he's doing it with fewer fingers.
As for piano, classical piano is out, I'm afraid. Some people may question that answer, but there are just too many incredible players out there, and the classical world is hesitant to accept anything but perfection (or close to it). However, piano in other styles is an option. Anything that doesn't have specific note requirements would be possible, in my opinion. So, jazz, rock… anything with chord symbols. It would be easier to do than guitar since the thumb is a fully used digit on both hands for the piano. I imagine you could do well if you were dedicated. The biggest thing is to learn (mentally) different styles and theory, etc., to compensate for any impossibilities on the instrument itself. Jazz/rock organ would be a good option; because too many notes muddies the sound, many players play simpler chords with embellishments that would be easier to accomplish and sound really good than with a piano where the sounds are easily distinguished.
My best advice is experiment a little bit, and then pick something and throw yourself into it. You can do things you set your mind to, it just might take extra time, effort, or modifications.
