If you wish to supplement protein for a workout, do so shortly before (as in minutes) and directly after the workout. 1 example would be like half a protein bar before the workout, and a protein shake after. Studies show a much bigger benefit of taking in protein right before and right after a workout contrasting with taking protein 3 hours later. You can google it easily. Some source papers I have can't be linked since I am auto logged in on a university account. There must be lots of public reference material on those studies.
Regardless, I am a firm believer in moderation and common sense. Do what works well for you. If you can't eat solid food during that time, lactose issues, whatever, there are 20 different ways to get what you need, and what you "need" depends on the person.