Don't be discouraged by small hands. I know many folks with extremely small hands who have become very accomplished guitarist. In some cases you may need to adapt in the same way as on piano and find alternative voicings for some chords.
A smaller scale guitar will also help. The biggest advantage is that the shorter the scale length, the closer the frets will be together. Scale length is generally specified in inches. Look for shorter. A 3/4 scale guitar, will, as the name implies, be about three fourths as long as a full size guitar. But even full size guitars come in varying scale lengths between different manufacturers.
Here is a company that specializes in smaller guitars. Small Guitars . com
To make your full scale guitar a short scale guitar until you can buy a short scale guitar, try putting a capo on the first or second fret and then tune the guitar to standard tuning and leave the capo on. This will shorten the scale of any guitar. The best capo for this would be something similar to a Paige Capo (see picture below).
By the way, your fingers might be short, but you mentioned that your fingers are also thin. For guitar, thin fingers are an advantage. I have short and fat fingers and with fat fingers it's difficult to avoid touching the string next to the one I am fretting and inadvertently muting it. Thin fingers allow for more precise fretting without accidentally touching nearby strings.