What is the daily protein requirements for a 55kg (21 years old boy) starting gym.does drinking a milkshake consisting of 3 eggs daily good or bad.

At least 2.2 gm/kg: Or one gram per day per pound of body weight. This is time-honored and seems to work. This is a more than is required for a man who does not exercise or want to gain muscle mass. You're free to take more but it will not cause you to get big any faster. There's nothing magic about eggs; get the protein in whatever form you like, trying to avoid grease & empty calories.

Whey for Resistance: 1.4 g/kg is minimum for athlete with weight training. Timing is important. You should consume a fast-absorbed protein source like "whey" protein immediately following your workout. This can be accomplished with protein shake with 3:1 (carb to protein) ratio. Eggs can be source of protein but use caution with raw eggs. Should get protein in 4-6 times per day along w/ prescribed carbs and efa's.