Hey! Happy new year!
I agree with what orangesuitcase said - focus on other benefits of exercise, not just the number on the scales - at least in the short term! It's best not to think of exercise as a quick path to losing weight, but as a long-term path to burning excess fat (along with zillions of other health benefits). Remember that most of the excess weight on your body isn't fat, it's just water (about 70% of it, or thereabouts - everybody fluctuates all the time - most people gain and lose several lbs every single day); and therefore most of the weight you gain and lose is also water.
What the PT is telling you to do makes sense. Eating a high protein and low carb diet (hopefully getting many of your carbs from lots of fresh fruit/veggies/salads) is a really good way to lose weight and burn fat, and it's definitely compatible with slimming-world. Please take a look at SW Red Days where large amounts of protein along with lots of fruit+veg is heavily encouraged. That's not to say you won't have a short-term gain after switching diet - by putting your body into the "shock" of diet change you might end up with some temporary water retention - just remember that it's only water, which just falls out really quickly and easily
You definitely shouldn't need to restrict the amount of food you eat with SW or feel hungry (but remember to drink enough water because sometimes we feel hungry when really we're dehydrated). One of the things which SW taught me is how many foods which I assumed were "healthy" or good for weight loss, which actually turned out to be really bad, including how much complete utter garbage is hidden in all kinds of innocent looking pre-packaged, shop-bought things like jars of tomato sauce or so-called healthy snacks made from cooked/dried fruit. these days I tend not to eat something where I don't know what it contains and what it's be doing to me, so I prefer to cook my own stuff where I can; and if I end up eating out at a restaurant I usually go for whatever looks "least bad", knowing that even the healthy salad is probably drowned in some high-fat-high-sugar dressing.
The way your body gains fat is mostly from the insulin in your bloodstream storing excess glucose as body fat. Protein takes a relatively long time to break down as glucose (Much longer than carbs! Refined sugars and processed carbohydrates are your real arch-nemesis here because your body soaks it up like a sponge), so by eating loads of protein your body should use it up as energy as soon as it's broken down into glucose, so it won't enter your bloodstream as excess glucose. That means there'll be nothing for your body to store as fat; in fact, it should be quite the opposite - you will probably have a deficit, thereby forcing your body to burn stored fat instead. So in a nutshell, that is the basic idea behind the SW Red days, and pretty much what your PT seems to be asking you to try.
It takes some effort to actually eat so much protein that you gain weight from it; and you'd need to end up practically living off an extreme "bodybuilder" type diet where you're demolishing two tins of tuna every day for breakfast, eating 6 eggs per day, a whole roast chicken every night, a pound of cottage cheese every day, etc. You're more likely to suffer kidney failure than weight gain by doing all of that. Just don't go overboard and you will be fine; also mix it up with loads of fruit+veg, try to drink several litres of water every day, and don't disrupt your sleep by eating late at night. Look for some nice recipes to avoid living off a load of bland/tasteless food where you're not resorting to sugar/white flour/jars of sauces/etc. The key to success is: Everything in moderation.
Exercise can be great for "pure" fat burning so long as you're preventing your body from gaining fat from your dietary habits. Of course that's why your PT wants you to cut back on the carbs - in reality your body really doesn't need many carbs to stay strong and healthy unless its for energy to do a lot of excercise. Otherwise, about 100g of carbs per day is the most which anybody really needs for their health and wellbeing. Some foods are bound to make you gain fat and/or negate the fat-burning benefits of exercise - typically those are the processed foods, sugars, refined carbs, lactose from dairy, etc - most of which is bad anyway because it tends to have little or no nutritional benefit to you whatsoever. So long as you avoid the foods which cause your body to store fat in the first place, then you won't be gaining fat from changing your diet. The quantity of food you eat is far less important than 'what' you eat.
Lastly, try not to look too closely at what's happening on any single given week; everybody hits a plateau sometimes, or has a week where they gain or STS, and the big picture is often hard to see until you look back over a long period of time, especially when you've had a bad week where it feels like losing weight is impossible. Just keep going and think about where you'll be in 7 months, not in 7 days
Good luck!
