I guess the TSH being 11 pushed the doctor to do something. More commonly the doctor will erroneously look at test results like your FT4 within range and say that everything is "normal" and you don't need medication, even when there are symptoms. So you are on the other side of that.
In your case you should make sure they test for both Free T4 and Free T3. The reason being that hypothyroidism is not just inadequate thyroid hormone, for which they use TSH as a surrogate test. Hypothyroidism is correctly defined as "insufficient T3 effect in tissue throughout the body due to inadequate supply of, or response to, thyroid hormone." So Free T3 is very important to know. Many doctors assume that if there is adequate T4 then the body always converts T4 to T3 as needed. That is very wrong. There are many variables that affect conversion. So it is important to know Free T3 levels. For the future you should keep in mind this conclusion from a recent, excellent scientific study: "Hypothyroid symptom relief was associated with both a T4 dose giving TSH-suppression below the lower reference limit and FT3 elevated further into the upper half of its reference range. " Frequently a hypo patient taking thyroid med will not adequately convert the T4 to T3, which then requires the addition of a T3 source to your thyroid med, in order to relieve symptoms.
As for the present, I really don't see the need for you to be on the T4 med. The most important consideration should always be symptoms, and since the Hashi's had not progressed to the point of causing symptoms, why did you need the med? A high TSH does not cause symptoms. TSH is affected by so many things that it is useful as an indicator of thyroid status only when it is at extreme levels. The doctor might argue that your TSH was at an extreme level, but then more importantly you had no symptoms and your Free T4 was right in the middle of its range. So the TSH was incorrectly diagnosed as hypothyroidism.
If it were me I would discuss with the doctor that the med has raised your FT4 to the very top of the range, and seems to be causing your current symptoms. I would ask to stop the med and confirm that symptoms ease and then defer any thyroid med until that time when your FT4 and FT3 are in the lower half of their ranges and you are having hypo symptoms.
Also for the future, recall the above definition of hypothyroidism as being related to insufficient Tissue T Effect due to inadequate supply of, or response to, thyroid hormone. So in addition to always testing for both Free T4 and Free T3, it is good to test for Reverse T3 at the beginning, along with cortisol, Vitamin D, B12 and ferritin. All are very important variables and need to be optimized. Excess Reverse T3 can offset the effect of T3 and create hypo-metabolic effects. Low or high cortisol can also cause problems for a thyroid patient. Vitamin D should be at least 50 ng/mL, B12 in the upper end of the range and ferritin should be at least 100. All of these affect the response to thyroid hormone and will become very important to you during future treatment.
If you want to confirm what I say, please click on my name and then scroll down to my Journal and read at least the one page overview of a full paper on Diagnosis and Treatment of Hypothyroidism: A Patient's Perspective. You might find this to be very useful for discussion if your doctor resists making these changes.
Something doesn't add up here. I would not expect you to have a Free T4 of 1.7, at the very top of the range, when taking only 50 mcg of T4 med. Were you tested for the antibodies associated with Hashi's, or did the doctor just assume that was the problem because of your high TSH? Were you having any symptoms at the time you were started on the 25 mcg of T4 med? What was your TSH and Free T4 before starting on the 25 mcg of med?
Before further discussion, what do you mean by "levels were in control"? Please post your thyroid related test results and reference ranges shown on the lab report. Do you have any other symptoms besides the diarrhea and stomach cramping?