I do not know your entire situation, however, please take steps to move up in your life. A nicer apt. etc. There are credit counselors who work for free f you look, they can hekp you budget.
As far as laundry, if it is not dirty or sweaty, do not wash it. Hang it on a hanger where air can circulate around it. I do this with work blouses 2 or 3 times.
If you hand wash, use a mild soap. I will sometimes handwash one or two item while I shower.
After get 3 towels, fold them in half sothey are nearly square. Wring out the handwashed item and lay in 1st towel. Roll the towel up tightly. Unroll and repeat with 2nd towel. Unroll and repeat with 3rd towel. Then hang on hanger in a well ventilated space.
You can also hang these damp towels to dry if needed.
Kudos on trying to save on the wash. I would keep a change jar, as laundry will have to be done occasionally.
As far as babies. They do not need cutesy, dress up clothes everyday. They can live in a diaper alone as or with a onesie or t shirt most of the time. They grow so fast, money is wasted on infant clothes.