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hey @zman , I’m guessing you are pretty new at guitar playing? The issue you are describing is very common for new players, regardless of the length or thickness of fingers. Lots of guitar players have short and big fingers…. As Albert said, you will gain flexibility and span as time goes to your practice. I would not advise you to spend lots of money buying new and expensive guitars just because they have a narrow neck, they can have other negatives with thicker fingers muting adjacent strings… But by any means, do go to try some at guitar stores and speak to sales advisers.
There are warm up exercises and stretches you can do to help getting your fingers more flexible, try to do them before your daily practice and with time and patience you will be pleasantly surprised 😉
Good luck