Hi shastanan!
I also have hypothyroidism, but I take Synthroid. It takes a few weeks to kick in. When did you start your medication?
I also was on Schwarzbein for a while. I used it to ease myself onto a lower carb WOE. I never lost any weight on Sch. For me, I have to count the calories and the carbs. I felt great on it, but didn't lose any weight.
After a lot of trial and error, I feel best on <90 g of carbs a day, 85-105 g protein, and less than 1550 cal. I usually get pretty close to these numbers. I try to never go over.
Eating all whole foods (although I do have low-fat versions of cheeses and try to watch the saturated fats), low GI fruits and veggies, and adequate protein (it's easy to eat too much protein - I really weigh and measure my portions - 3-4 oz lunch and dinner) gives me lots of energy to exercise every day.
In fact, it was the Sch. book that prompted me to begin in earnest a weight - resistance exercise program. I owe my ongoing success to the weight exercises, as well as walking (my dog) 35 min 6 days a week.
I also would like to add that when I did really low carbs, even up to 70 g a day, I had no energy, felt 'out of it' with brain fog, and became depressed. So, keep an eye on your carbs. Too low may be no good for you, as well.
I hope you find a plan that makes you feel well and that you can live with.