Sims won't change clothing

I'm not totally sure I understand you right but if you choose change outfit, you only have the options to change into what you gave your Sim to wear in the first place. There's no option to buy anything like in Sims 2.

What you need to do is choose Plan outfit. This will take you back to CAS where you can give your Sims a different outfit or add another one (there's a liitle + sign above the icon where you choose what kind of outfit to give them. Afert you did that, it becomes part of change outfit.