Join Date: Sep 2011
Location: Cincinnati, Ohio
Bikes: '74 Schwinn Le Tour (x2), '83 Bianchi, '96 Trek 820, '96 Trek 470, '99 Xmart Squishy Bike, '03 Giant Cypress
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I am the same height as you, and a 23" bike would have me on a pretty long seat post, with a good drop to the handlebars. If you haven't built up your core strength yet, you are going to be putting all of your weight on your hands, which is going to cause numbness pretty quickly on flat bars.
Pull the stem up to it's maximum height and see if that helps the hand numbness any. If you are at your max height on the stem, you may be able to get your LBS to swap for a longer one, or you can find inexpensive ones online for under $20. As your weight drops and your strength improves, you'll probably find that you can handle leaning forward/down much more than you are currently comfortable with.
Also, I'll second the comment that if you have knobbies, you'd be happier with a more road-oriented tire.