Immediately when? After waking up? Eating lunch?
Or do you mean "immediately post workout"? If so, yes, its ideal to get protein into the body IMMEDIATELY.
Why does it take you two hours to eat oatmeal? Even when I cooked 1 cup raw oatmeal (for bulking) I downed it in 20 mins or less. Any longer and it was cold paste.
I would drink your shake, and eat the oatmeal 'plain' (and faster). After 2 hours of grazing on oatmeal, its time for the next meal.
in fact its common to have a post workout shake, and then 60 mins later, a whole food meal (steak n potatoes are my favorite).