Yup. 32 oz is too low a water intake even if you're not losing weight. Low-carb diets are very diuretic; it's essential to replace the liquids that the diet makes you get rid of. If plain water is hard for you, try herbal teas (except medicinal ones). (The evidence that the good Dr. A. used to prohibit regular herbal teas didn't impress me).

Along with the water you lose go electrolyte minerals, notably magnesium and potassium. You can get potassium through pills or a potassium broth, but you'll probably have to get extra magnesium through pills.

During my weight loss, I had a goal of 100 oz/3 liters of water and herbal tea per day.

If upping your water/herbal tea intake doesn't relieve the soreness entirely, try taking 5 g of glutamine before bed on workout days.