Is TSH the only thing that's been tested for thyroid? You should also be getting Free T3 and Free T4 tested as those are the actual thyroid hormones, while TSH is a pituitary hormone, whose only role is to stimulate the thyroid to produce hormones... TSH often becomes irrelevant when one is on thyroid hormones, but yours is quite high, indicating hypothyroidism. Free T3 and Free T4 would confirm this.
Most of your symptoms sound like you could certainly use an increase in your levothyroxine dosage... High cholesterol is also a symptom of hypothyroidism, and your bears out the need for an increase in medication, as does your weight gain, fatigue, anxiety, etc
Ferritin is the iron storage hormone and does indicate the amount of iron in your body... you should have a complete iron panel to make sure hemochromatosis is not causing your high ferritin levels. High ferritin is also caused by inflammation in the body, so a cold, flu or some other illness could easily explain the high levels.
Have you ever been tested for Hashimoto's Thyroiditis? Hashimoto's is an autoimmune condition in which the body erroneously determines that the thyroid is foreign and produces antibodies to destroy it. This process can produce inflammation, which can also increase ferritin levels.
The chances of a malignancy are extremely slim...
Healthy fats, such as those found in olive and coconut oils, nuts and nut butters, seeds, lean meats, fish, etc are necessary for a healthy diet and can actually help ease inflammation and can help with weight loss, once thyroid hormone levels are stabilized.
You're welcome; that's what I'm here for... if there's anything more I can help with, feel free to ask the questions, here and either, I or someone else will do our best to provide answers...