You appreciate guitar enough to have found your way here. Good sign :)
I've seen people with short fingers play a pretty mean guitar. Jack is right if a full size guitar is too large there are smaller scale guitars 3/4 scale may be up your alley. Warmup and gentle stretching also helps loosen up your fingers, hand, wrist and forearm.
Chords are awkward to us all when we first learn them. I'm still finding some new chords awkward after 20+ yrs playing ! Additional tip when people first grab a chord book or look in the internet for chords - they jump right into the 'full' shapes for G Major, F major and bar chords etc. A beginner mel bey book will take you thru simpler chord shapes first where you hold only 1 or 2 notes in combo with an open string. You could try those first from the chord book then Triads until your fingers are more stretchy, which happens over time. Any easier ?