Hi LeighAnn!
Actually, about 60% of your body weight is water, even if you're not retaining extra water. Surprising, I know! If you're genuinely at 38% fat, then you have 54 pounds of fat and 89 pounds of lean body mass. Lean body mass (LBM) is everything in your body that
isn't fat, so it's all that water, plus blood, skin, muscle, bone, hair, organs etc.
In answer to your question, 10 - 12% body fat is considered "essential" for a woman. If your LBM remained unchanged at 89 pounds, 12% body fat would put you at an even 100 (89 pounds of LBM and 11 pounds of fat). So you wouldn't want to weigh less than 100 pounds at your current LBM, which is 43 pounds less than you are now. That's the LOWEST you could ever weigh and still remain healthy.
But in reality, 12% body fat is very difficult to reach and sustain for a woman -- it's the rock bottom floor you don't want to go below, not a target! Check out these body fat guidelines from ACE (the American Council on Exercise) and see what might be a more realistic target for you:
Essential Fat: 10-12 percent
Athletes: 14-20 percent
Fitness: 21-24 percent
Acceptable: 25-31 percent
Obese (or high risk): over 32 percent
As for visible abs, a woman generally needs to be in the lower teens of body fat.
At your height and weight, right now you're more undermuscled than overweight. Your 89 pounds of LBM is pretty low for someone of your height (I'm only 1/2 inch taller than you but have about 28 more pounds of LBM). Rather than worrying about on losing "weight", I think you'd be a lot better off by focusing on building muscle while losing fat. You could weigh 143 pounds with a body fat percent of 20% and look completely different than you do now! And you'd probably be two sizes smaller. Without losing a pound on the scales!
Since you've just joined a gym (good decision!

) and probably met with a trainer to have your BF % done, hopefully you've been set up with a program of cardio and weights designed to do exactly that: build muscle and lose fat. Don't worry about what the scale says because you don't need to lose a pound of "weight" - just focus on adding muscle and losing fat and you'll reach your dream body.