I'm trying to lose my tummy, I am following a plan. I eat accordingly and stay away from sugar, I do have protein shake post workout, and in work out have my BCAA. It's been a month, I take 1-2 days off from gym also I try to swim (although I'm learning), my weight has been fixated on 80 kg. The program I am following make sure you lose 2-3 pounds per week. Given everyone's body is different and what the person can lift weight I cannot. Can I blame protein shake or BCAA from keeping me shedding the weight?
You are not losing weight because you your calorie intake is greater than your calorie expenditure.
While this isn't directly attributable to your workout shake, they still have calories - albeit nearly 100% protein.
If you which to lose weight but arent, you need to adjust it so you use more calories than you consume. This can either be done by additional exercise in the day without increasing your calories to compensate or by reducing your calories further.
While the protein shake may seem like an easy target for reducing your calories, as mentioned in the comments, protein is important when eating at a calorie deficit. Instead, look at reducing your consumption of hidden sugars in your day such as soda, fruit juice or overly sugary caffeine drinks. Also consider slight decreases in your portion sizes and reducing snacks.
Its not a simple as following a plan because someone says so, and expecting it to work perfectly. This isn't a movie. What worked for them might not work for you, and you are intelligent enough to realize this I see.
Staying away from sugar will not be the defining factor in your weight loss goals, what will aid you in your weight loss goals are ACTUALLY working out, which i didn't even see you mention.. and listening to what @LarissaGodzilla just told you.
You should start to see weight lose within a week, if you are doing it properly. A couple of pound a week, is realistic. Look at your diet, and exercise program.
There are app that will help you count calories, and help you workout how many calories you require to lose weight. Myfitnesspal is pretty good.
Don't go lower than recommended, otherwise your metabolism will slow, as your body will think its being starved.