It sounds like your handlebars are too wide, but just getting more narrow ones may not solve your other problem of reach. Its hard to say from what you wrote - are you over-reaching? stretched out, elbows locked, etc. or is it just your hands that are too small?
If you are way stretched out it may be more than just the handlbars that is too big for you. If its just a matter of hand comfort you can play around with the positioning of your shifters to try to get a more comfortable hand position (but do check out more narrow bars too - they may help even if they are not the total solution)