It isn't protein that elevates creatine, a high protein diet would elevate urea.
Creatine is a high energy molecule carrier (ATP) in muscle tissue, so eating meat = muscle, increases creatine and its breakdown product, creatinine.
Also the amount of muscle you have will reflect on the amount of creatine. More muscle, more need for creatine, more creatine, more creatinine.
I am not sure how long the effect of cooked meat lasts, I would think/recall four to six hours.
Has your GP suggested that you have repeat bloods in a few months?