A few days ago my shoulder became sore/strained because of improper form while exercising. However, there is only mild aching and it is getting better day by day. I have been doing bicep curls, mainly hammer curls but also some other variations, along with chin ups and have not noticed it hurting that much really and don't believe there to be much shoulder movement invloved. Are bicep curls okay to do with a sore shoulder?
Yes, by all means.
When you do bicep curls, your primary goal is to stress your biceps, and as few other muscles as possible.
Find a position and trajectory in which you only put stress on your biceps, so that your deltas are involved very mildly, merely to keep your arm position steady, not to help it pull the weight. It is impossible to avoid using the shoulders entirely, but minimizing their involvement to make the aching tolerable is quite possible.