Who said they were getting proper protein from their meals?
You can easily eat WITH your shake but remember not to overconsume calories, and note which macronutrients you are taking in at once (a shake will usually constitute all of your protein for a meal). I’ve taken a shake with an apple a few hours before bed many more times more than once after a late workout with no ill effects. The purpose is to feed your body and replenish nutrient stores.
As Michael said if your getting the proper amount of protein from food you might not need a potein drink. Also, be aware that the body can only synthesize about 20 grams of protein effeciently, and there’s no added benefit to taking more at one time. If you are going to eat and take a protein drink, I would wait at least 2 hours in between. This is information that has been researched by the National Strength of Conditioning Association. Please be cautious if you have any type of health issue.
Hope this helps.
Since you are consuming the shake after your workouts then I am assuming that you are doing it as a an exercise recovery drink. Your best bet is to consume the shake by itself so your body can easily absorb the macronutrients (e.g. protein and carbs) and utilize them asap. Make sure your shake also contains some simple carbohydrates to help aid in muscle recovery. If your protein shake is low carb then you could eat a banana with it (or blend it in with the powder) or add 1-2 tablespoons of honey with it.
Hope this helps!