Completely normal, but not a necessity. It could be in spite of you doing everything right or you might be making major mistakes. It's hard to tell from what you're writing.
I'm going to make a series of statements. Not all will apply (hard to tell by that information) and it will not include everything there is to say, but I'm sure some will. Also, I will number them just so they are easy to reference, not because that order has any meaning. Here we go:
Your weight fluctuates constantly, so weighing yourself twice has no meaning. You drink or eat more one day, you go to the toilet, you weigh yourself perhaps once after lunch and once after dinner - completely different results. In my experience fluctiations of 3kg or more are completely normal. My solution to this problem is getting on that scale at the same time of day every time, I do it right after getting out of bed in the morning. Mid day, the results fluctuate way more.
You want to lose fat, not body weight. Most of your body weight is in water. You will find that once you start training or changing your nutrition, your weight will fluctuate like crazy because of water. Perhaps your body starts storing a bunch of water now. Additionally, you might drink more now that you train, eat more vegetables (mostly water) and so on. Changing stuff = weight fluctuation. You've changed a lot by eating that powder stuff, even if everything else stays the same. This is why you shouldn't weigh yourself constantly. One day you will leak a lot of water and lose 1 kg at once, the next day the opposite happens. Weighing yourself once a week = great. 14 days = better if you are patient. You don't seem patient, so once a week. Generally speaking, the fat loss should be constant - but you cannot measure that easily, the weight loss will be less constant.
Your nutrition could be way off. There is no way to tell from your information. But what some people do when starting to work out is two things: a) feel a lot of hunger and b) think they now deserve extra food. This can lead to starting to work out = getting fatter. You are not really overweight, so since you are not a 150kg man running for the first time, you will not burn way more than you are able to eat. You make no mention at all of what you eat which tells me: You have no clue what you eat. Start tracking your calories or, if you don't care about food, follow a meal plan. There are other options, I will not mention them all, but just not eating dinner doesn't mean caloric deficit = losing fat. You can even eat only once a day and still gain a lot of weight. The frequency doesn't matter but the total caloric intake does. So start tracking.
The only reasons I can think of to take protein powder are the following: a) You absolutely don't have the time or appetite to eat something decent - doesn't apply most likely or you would be underweight. b) You are vegan and don't like the vegan protein sources or travelling and have no other protein sources. Also there are some allergies that might prevent you from eating certain protein-rich foods. c) You are a professional on steroids. d) You are a beginner that doesn't know what he is doing and needs to learn by making mistakes. Protein powder is mostly marketing. If you have a decent, normal human nutrition, you don't need that stuff. Especially at the beginning. Better learn how to eat properly. This comes back to point 3, track and think about what you eat and stop wasting money for protein shakes. They are horrible for losing weight because you then drink a bunch of calories (about as much as sugar, think about 50g sugar in a drink - that's madness) that leave you hungry. Better eat lentils, fish, whatever you like instead. They make you full, have something called micro nutrients and are great protein sources. My advice is that you stop wasting your money and calories on protein powder.
Be way more patient. This stuff takes time. I don't know, maybe they have some sort of sales pitch at that gym - lose weight in three days or we don't know what we are doing. I don't know, but I find it strange that they didn't offer you an ex. Usually, you start losing weight rapidly at the beginning and then stop thanks to water management, see point 2, but that depends on what you did beforehand. I know someone who was sick just before starting to lose weight and didn't lose anything for 3 weeks and then suddenly dropping a lot. I mean give it a month of doing it right before you can really judge that you are moving in the right direction.
I've had a couple more points that I forgot. Please feel free to add stuff via comment, I might edit.
Long story short: Weigh yourself less often (or not, but stop overemphasizing what the scale says), start tracking nutrition and be patient. It's really impossible to tell if you are doing stuff correctly from your information, but I can tell you how to do it right.
Losing weight is basic physics. You need a certain amount of kcal throughout the day, let's say 2500 in your case - if you don't have a demanding job. You work out, now it's 3000. A caloric deficit of 500 is plenty (the post is too long already, don't go beyond that period.) So you need to eat 2500 kcal every day. Get that via normal food, it shouldn't be hard to get enough protein that way. I would track the amount of protein as well - if you do this via app, a calory counting app should do that automatically. How much exactly you need is debatable, but it's less than what people tell you. You can optimize that later if there is an issue. I think 1.4g per kg of body weight is the highest credible number I've ever found. But my point is that if you don't get enough protein, your nutrition is off. If you need a 50g shake every day, you should eat different food. Because if you are lacking in that area, my guess is that it's not just your protein intake that is off.
The remaining 500kcal, well, your body will obviously get them from reserves - e.g. fat. You cannot cheat this. If you are in a 500 kcal deficit every day, you will lose body fat. How much is that in kg body weight, the thing that you track and worry about? Well, really, it depends. Some say about half a kg every week. I think that's a good number in general, but water weight and so on. What do you lose in 4 days if we take the 500g a week? Well, about 300g. Is your scale even that accurate? You drink a glass of water and you weigh 300g more. You cannot really tell how much you lost after just 4 days.