Far more important than that information is the symptoms you have, if any, and your Free T4 and Free T3 levels. So please tell us about any symptoms, and also if you have been tested for Free T4 and Free T3, then please post results and reference ranges shown on the lab report.
In the words of an excellent thyroid doctor, "The free T3 is not as helpful in untreated persons as the free T4 because in the light of a rather low FT4 the body will convert more T4 to T3 to maintain thyroid effect as well as is possible. So the person with a rather low FT4 and high-in-range FT3 may still be hypothyroid. However, if the FT4 is below 1.3 and the FT3 is also rather low, say below 3.4 (range 2 to 4.4 at LabCorp) then its likely that hypothyroidism is the cause of a person's symptoms."
So your PCP did the right thing by starting you on thyroid med, since you have Hashi's and your FT4 and FT3 are in the lower half of their ranges which, along with symptoms, are indicative of already being hypothyroid. On the other hand the Endo apparently does not want to do anything until your test results exceed the reference range, which is wrong for you.
A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results. If you want to confirm what I say, I recommend reading at least the first two pages of the following link, and more if you want to get into the discussion and scientific evidence supporting all that is recommended.
Note in the link that a hypothyroid patient should be given thyroid medication adequate to eliminate signs/symptoms of hypothyroidism, without causing any signs/symptoms of hyperthyroidism. This is quite different from the usual approach of medicating enough to just bring the TSH down within the range. That practice leaves many hypo patients inadequately treated.
Also realize that the 25 mcg of T4 is a small starter dose. It will not do much, if anything, to raise your levels and help with your symptoms. This is because the med will cause your TSH to drop and thus stimulate less natural thyroid hormone production. Since serum thyroid levels are the sum of both natural thyroid and thyroid med, as stated in Rec. 10 on p. 13, "Only when TSH is no longer stimulating natural thyroid hormone production, or is suppressed, will serum thyroid levels reflect further increases in thyroid medication." 37
So you are going to have to find out if your PCP is willing to treat clinically, as described. If not, then you will need to find a good thyroid doctor that will do so. If the PCP needs some persuasion, perhaps a copy of the link will work. Also note in the link the importance of Vitamin D, B12 and ferritin, and get those tested and then supplement as needed to optimize.
Most doctors have the "Immaculate TSH Belief" and only pay attention to the TSH level, which doesn't work for many patients, for a number of reasons. If they go beyond TSH it is usually only to test for Free T4, and then they use "Reference Range Endocrinology" and will tell you that any thyroid test that is within range is adequate. That is also wrong, due to the erroneous assumptions used to establish ranges, and the assumption that everyone is alike in their need for thyroid hormone. This is all explained in the link I gave you above.
No, missing the two days will not matter. What I think you need most is to give the PCP a copy of the link and ask him to read it and see if he will treat clinically, by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. If not you will need to find a doctor that will do so.