Not worth it. Balance your diet and eat as much as possible with the right BJU ratio. A protein shake only gives you 20-25 extra grams of protein. Without sufficient exercise and diet, it will not give any effect.
Unfortunately, a protein shake will not give the effect you expect from it. It is only necessary if you work out in the gym, while focusing on strength exercises there. And then only when, for some reason, you do not consume enough protein. For example, if you are a vegetarian.
In your case, you need to pay attention to increasing your daily calorie intake. The easiest way to do this is by consuming more carbohydrates, namely buckwheat porridge, pearl barley, pasta and the like. And read about the glycemic index. If you certainly want to use something from sports nutrition, then take a closer look at a gainer. It is a high-calorie protein-carbohydrate blend. Just do not overdo it with it, as there is a risk of gaining a lot of fat.
So, to summarize: You do not need protein - in your case, it's money down the drain. Eat more porridge (seriously and literally), if money burns your pocket, then buy a gainer, not protein.
A protein shake is worth drinking only in one case - if you have absolutely no time for a meal. If you are thin, then you can safely eat your daily protein intake (2-3g per kg of body weight, although different sources have their own rate). The increase in mass is a surplus of calories, if you gain your norm in protein, you simply increase the carbohydrates. Exercising will help you wake up, stretch, but definitely not build muscle. It is necessary to train with free weights. I advise you to watch the video blogs of Denis Seminikhin on nutrition and Boris Tsatsulin, there are all the answers to the standard questions of beginners.