What should I use post work out on my skin?
Glad you asked this and it depends somewhat on what time of day you work out. You don’t need to reapply the sunscreen if you work out late in the day or when it’s dark clearly.
As for washing, just rinse your face after exercise without any cleanser (unless you are super oily). You’re right, washing too much will dry you out. You can just rinse, reapply a little moisturizer appropriate for your skin type and sunscreen after that, if needed. Moisturizers.