I am a 22 year old female and I also have hashimotos. This diagnosis doesn't mean you cannot run, you are not sentenced to that if you train and live appropriately.
Remember, whether or not your hashimotos is under control doesn't JUST depend on your labs/bloods, it also depends on how you feel on a day to day basis/how inflamed you are as this is an illness where the higher your inflammation markers, the worse the syptoms will be. Now, it probably is isn't a good idea to go running long hard miles and pushing your body to the limit if you are in the midst of a hashimotos flare up (eg: if symptoms are bad and the inflammation levels are high).
However, this doesn't mean quit running at all. It just means that befire attempting to train for any athletic event, your body needs to be in a place where your symptoms/inflammation levels are under control. Once they are, then you may go out and increase your milage but as with any chronic illness, it means that your body has to work a little harder and may take a little longer ti adapt to the increase of milage so you must make sure you are fuelling appropriately, hydrating appropriately and resting appropriately. People in our condition need more rest days than average runners also.
Please take it easy because you do NOT want to end up overtrained when dealing with hashimotos. People in our condition are more exposed to over training so sometimes it is best to take more rest days than you think you need.
My hashimotos was terrible last year- even though my TSH/T4 were umder control because of the levothyroxine- my inflammation levels were still high. I wasn't eating because my digestion was so bad, I wasn't sleeping because my hormones were all over the place and I could hardly get out of bed because the fatigue was that bad. I made a huge mistake of using 100% of my daily energy to get out and run, and because I was basically forcing my body to do this when it was already stressed with the hashis- I got overtrained FAST. I went from cruising on daily runs of up to 10 miles at 6:30-8:30min mile pace to being capable of absolutely nothing. 1 mile at any pace would completely wipe me out. You do NOT want to end up like this so I suggest you take the same approach to easing into marathon training and I did easing back into running.
I had no choice but to take a few months off running so that my body could return to a more rested state. Assuming this is where you're at now, I suggest you easy into training very gently (like I did):
For three weeks I did two runs a week, for. the next three weeks I did three runs a week, for the next three weeks I did four runs a week, and so on. I am now working out 5-6 days a week with no problem. But I started off SO LIGHTLY at first, I was even told by a few running friends that I was half arsing it but if you have an illness that compromises your hormonal health and ability to adapt, which hashimotos does, them the best approach to take at first is to take an easy half arsed approach and spend a while in that phase as this will greatly reduce long term fatigue. Once you have done that for a while and you feel consistently energetic and ready to train, then you can start a normal base building marathon plan (if you are following a generic marathon training plan then perhaps give yourself an extra week in each phase and an extra rest day in each week)
I cannot stress this enough but you must nourish and rest properly, it's importamt and key to every runner but it becomes ten times as importamt for those of us with hashis. When dealing with this, you MUST get to know your own body inside and out. It is key. I have discovered this year that both dairy and gluten aggrivate the inflammatory markers which trigger my hashimotos to flare up so I have cut them out of my diet and as a result I am performing better.
Getting tested for intolerances (maybe with tests or with a nutritionalist who can work with trying out a FODMAP diet with you) is a good idea when you have a compromised thyroid/immune system. It will also help you determine the right nutrition for your marathon training.
If I didn't eat a diet jam packed with nutrients and minimal toxins/chemicals, wasn't gluten free and didn't rest for at least 7 hours per night - there is absolutely no way I'd be running at all right now.
Taking a probiotic (and switching it round every couple of months) is also a good idea. Along with bone broth for extra immune support.
When all said and done, what I'm trying to say is nourish properly and if you feel tired then back off until you feel you can spring back. I fought through the fatigue and I ended up having to cancel a half marathon last year as a result, it could have been avoided if I just took the days off and rested when needed. As long as you listen to your body and do things very gradually you will be fine. Good luck with your training.