Actually, get a third or fourth opinion, if you want. If you want to play the guitar then no set of fingers is too small. Of course you can buy a smaller guitar, but also there are other tricks as well - position of the guitar, style of guitar, etc.

You didn't mention what style of guitar you like. Classical guitars typically have 2 inch wide necks, but because they are cradled in you lap you have a much different angle to reach around the neck. Steel string guitars have narrower necks, but are typically held at a different angle (the neck being more parallel to the floor). Also, if you have the guitar of your dreams and you do not want another guitar or cannot afford one, you can take yours to a good luthier or repair shop and have the back of the neck on yours reshaped to allow your hand a better reach.

I have smaller hands than normal (I think) and it causes me no amount of grief. On my classical I have learned that if a certain position is just too painful, I can usually delete notes (say, in a barre chord) or make other slight adjustments. With my steel strings I can either use a capo (the higher up the neck you go the frets get closer together) or transpose the key so I get easier chords for my little hands.

Most important lesson: keep playing and keep trying. If you love the guitar don't give up. You might want to play the banjo too, but never accept defeat just because someone told you to.

Cheers,

Freightdawg