Why not start out by posting your very normal T3 and T4 results, and be sure to include reference ranges, as those vary lab to lab and have to come from your own lab report. Also, be sure to tell us if those are Free T3 and Free T4 or if they are Total T3 and Total T4... They aren't the same tests and don't give the same information. Typically, any test that just says T3 and/or T4, without specifying "Free", is Total, which is considered obsolete and not very useful.
TSH is affected by many variables and can vary by as much as 75% over the course of a day, tending to be lowest in the morning and highest later in the day.
Are your mother and sister, both, on replacement thyroid hormones?
It's not good to eat processed foods, so you try eliminating the processed foods, such as breads, crackers, processed cereals and other baked goods and eat only whole foods and see if you have the same reactions. When I say whole foods, I mean fresh/frozen fruits/veggies that have no flour, preservatives and other added ingredients.
Symptoms can apply to more than one condition and it's very possible that you have celiac (gluten allergy) or gluten intolerance or are sensitive to other ingredients in preserved foods. Some people are also sensitive to dairy products so you might consider eliminating those to see if you do better.
I've read that a small part of the population has Hashimoto's without antibodies and can be detected via ultrasound, however, that remains, somewhat, controversial. Autoimmune conditions tend to run in families, though not every member of a family will get the same condition - for instance - I have Hashimoto's and Pernicious Anemia, my son has Type I diabetes and my daughter has Lupus - all autoimmune.
That said, only having high TSH, does not constitute hypothyroidism. TSH is a pituitary hormone, not a thyroid hormone and as noted above, can vary by as much as 75% over the course of a day. You're only hypo if your Free T3 and Free T4 are inadequate. Once we see your actual Free T3 and Free T4 levels, we can help determine whether you need replacement thyroid hormones.
Check out the WHole30 diet. it is basically the Paleo diet but more strict for 30 or so days (Hence the name) so as to determine which foods you may be intolerant or allergic to.
This food thing and/or gluten is for the most part separate from they THyroid. But it is still important to find out if you have allergies and intolerances in order to help feel your best.
I agree with Barb135, please post your results with the ranges. it is not uncommon to be within the "normal" or "reference" range but still feel poorly. This is because they establish the ranges incorrectly. You need to be about 50% or higher in the typical ranges to feel well. If you are below 50% in either or both Free T4 and Free T3 and you are symptomatic, and feel poorly, then a trial of medication would be reasonable to start if, and that is a big IF, you can find a Dr to allow you to take thyroid replacment. This forum is littered with people who struggle in the catch 22 where they are in the normal range but feel like crap. Often leading them here desparate for an answer. And when they finally start getting replacement thyroid hormone they begin to feel better. The "rub" is finding a Dr who will treat you when you are in the "normal range".
You have to be your own best advocate. Do NOT settle for someone else who doesn't have to live inside your body every day tell you that you are "fine" or "normal" when you KNOW you feel like crap!
Educate yourself on THyroid. Read a lot here and other places and learn for yourself. You are a human being just like the Dr. is a human being. Don't be intimidated by the two letters "MD". Sure they have a credential. But you can get and learn information just as well as they do. And unlike a Dr. who often times needs to understand 1,000 differen things. You can focus like a laser on the single issue of THyroid. You tell me who after a couple of years will know more about thyroid. Someone who studied it 10 or 20 years ago in med school. Or someone who feels like crap and learns and studies about it daily for the last several years?
I'm not saying to no respect Dr's. I'm just saying do not settle for answers that just don't seem to fit. And be your own best advocate and get your own education and stand up for yourself. if you don't, chances are no one else will stand up for you either!