Ok, that makes sense, and you still sound like me
These plateaus are normal, I believe. When I check my app I notice that between Sept. 4th and Oct. 31st, almost 2 months, I lost as much as ... wait for it... a whopping 1,2kgs!! Mind you, we could both be doing something wrong
On the other hand, when you gained weight, did you notice if this happened in steps too, or did you, like most of us, avoid the scales like the plague?
I weigh myself almost every day. My trick is to blatantly ignore the mornings when I've gained a kg or even two. I only open my app and make an entry when it's lower than it's ever been before? Cheating? No, I don't think so, because no matter what I'm still losing weight, sometimes very slowly, and then, like yesterday, suddenly I'd dropped 1 kg from the day before. I was too much of a coward to weigh myself today
If you read my bio you'll see that years ago I lost a massive 35kgs. I'd lose 1 - 1.5 kgs/week, so when I started LCHF I expected the same kind of results and was disappointed. Some say that my rather slow rate of losing weight could have to do with previous yo-yo'ing, and I'm sure that it also has to do with my being 12 years older.
As for exercise I'm not so sure it makes much of a difference to weight loss. It does to general health, no doubt, so going for walks and swimming is great for BG control, but in my experience not so much for weight loss.
However, if you're still not sure if you're doing something wrong maybe hop over here and read.
https://www.dietdoctor.com/q-a-not-losing-weight-lchf