Dry skin can make it prone to acne because of the weakened skin barrier. Apart from choosing the correct facial wash (which you definitely should have), a suitable moisturizer is very important as well.
I agree with Dr Israr's approach to having two different facial washes, and also Dr Shane's clinical approach to properly assess your skin condition before making a recommendation.
There are acne face washes that have 'acne curbing ingredients' without being too dry at the same time (with the use of some emollients). I would highly recommend using one of those.
Hope this helps!
