short answer is: IF you are getting enough protein from your diet (and I don't think you are) then you don't need a protein shake, no. Especially since you're just starting.
Though from the perspective of someone trying to lose weight, a protein shake may be a good thing for you - consider it a VLC 'diet shake', and take it post workout.
I'd need to know more RE your height, weight, etc etc.
AND training a muscle or muscle group 3 times a week is not smart. Could you please explain what exercise routine you're running??
W.A. AMATEUR STRONGMAN
Axle clean-press: 100 kgs (220 lbs)
Bench press: 135 kgs (298 lbs) - 1st PL meet 16th October 2011
Deadlift w/Barbell: 180 kgs (397 lbs)
Deadlift w/Hexbar: 225 kgs (496 lbs)
Farmers walk: 240 kgs (530 lbs), 50 feet
Front squat: 100 kgs (220 lbs)
Log clean-press: 100 kgs (220 lbs)
Strict OHP: 85 kgs (187 lbs) 3 reps
Tyre flip: 260 kgs (573 lbs), 100 feet