Yes, dieting very possibly can make things worse. As I said, you need calories to convert the T4 you're taking (storage hormone) into T3 (active hormone).
And if calories are in short supply, what's available goes to essential activities like breathing and digesting, and heart beating, moving around etc. Conversion is way down on your body's list of priorities, funnily enough.
And, if you cannot convert your T4 to T3, you get more and more hypo, your metabolism therefore gets more and more sluggish, and you put on even more weight.
Exercising is even worse, because not only does it use up your precious calories, it also uses up what little T3 you do have. You've already said you can't exercise because you're so tired. Well, that's because you Don't have enough T3. If you exercise, you'll have even less. And then how will you manage the rest of your living, like keeping yourself clean, and feeding yourself? You can't. Just remember that every movement is exercise in the strict sense of the term - even just breathing.
It's low T3 that causes symptoms, not low T4 or anything to do with the TSH as doctors seem to think. So, the less T3 you have, the more hypo you are, the more symptoms you have, and the more difficult it is to lose weight.
So, at this stage in your journey, 'diets' and strenuous exercise are most definatley not recommended. You need plenty of good food and just gentle movement like walking or yoga, to keep you from rusting up!
To be able to lose weight, you need good levels of T3. And I bet yours are rock-bottom at the moment.
After just one week, you really can't expect anything much to improve. And trying to hurry things up, and taking short-cuts is just going to make things worse - remember the saying : more haste, less speed? Everything to do with thyroid is slow!
So, patience is the number one rule. Number two, is good nutrition. Your nutrients are probably rock-bottom, also. You should ask your doctor to test : vit D, vit B12, folate and ferritin.
When we are hypo, we usually have low stomach acid, which makes it difficult for us to break down our food and absorb the nutrients. However, those listed above (and some others) absolutely need to be optimal for your body to be able to absorb and convert the hormone you're giving it.
Which is another reason not to restrict your food intake. The less you eat, the fewer nutrients you have. And nutritional deficiencies will also make it difficult for you to lose weight.
So, it's not just a question of popping a little white pill every morning, and waiting for the miracle to happen, as doctors think, there are lots of other things to consider, too.
Hope I haven't over-loaded you with information, there. lol It's a lot to take in, in the beginning, I know. But we are always here, and you can always ask - and reask - any questions you have.