Hair products such as conditioners oils and hair masks are a good idea when scalp cooling as they can help to maintain the quality of your hair. Products such as mousses, gels or hairsprays that can make your hair sticky are not advisable as they can make your hair much harder to manage and possible put address weight or stress on the follicles.
Generally there isn't a problem using a medicated shampoo that was prescribed prior to treatment, but we would always advise talking to your clinical team for confirmation.