Your doctor is dosing your thyroid medication, based only on TSH? For that reason alone, you need a new doctor. Dosing thyroid medication based only on TSH is like trying to shoot a moving target and TSH doesn't even correlate with symptoms, at all. You need to have FT3 and FT4 tested every time you have a TSH test. Those are the actual thyroid hormones, with FT3 being the one that's used by individual cells and correlates best with symptoms.
The time span you're dealing with is from January 2012 to October 2014, so that's over 2 yrs - the weight loss isn't huge over that time, but at your age, you shouldn't be losing weight at all when you weren't overweight start with...
Are you supplementing testosterone to bring your levels back up? That needs to be addressed before it gets any worse.
Even though your Vitamin D was 35 and "in range" in Sept 2014, it's still way too low. It needs to be at least in the range of 50-60 in order for symptoms to be alleviated - just "in range" isn't good enough. How much vitamin D are you taking on a daily basis?
Have you been tested for diabetes? Type I diabetes can cause some of the symptoms (specifically the weight loss) you have. It can also cause depression, mood swings, fatigue, severe hunger, etc. You should ask your doctor to test fasting glucose as well a glucose tolerance test and a hemoglobin A1c.
You should also ask to have a vitamin B12 test done... vitamin B12 deficiency can cause horribly fatigue, depression, brain fog, etc.
Your depression may not warrant Prozac - it may only need adequate thyroid hormones, vitamins and minerals. Prozac does tend to cause tiredness and when one already had fatigue the last thing you want is a medication that exacerbates the issue.
I think you should ask to have testing done to make sure your pituitary gland is working properly... since you already know you have low testosterone and hypothyroidism.. testing for diabetes will take of that part. That leaves adrenal testing - ACTH, cortisol, DHEA, etc.
What are your thyroid hormone levels - Free T3 and Free T4? Please post them, with reference ranges, which vary from lab to lab and have to come from your own lab report.
Free T3/T4 haven't been tested since my original diagnosis.