Does your doctor have a online portal that you can message and ask about your latest lab results? Or better yet a nurse in their practice that you can speak with today and request that your results get reviewed by your doctor? In my own experience (in California) as long as you have had some sort of visit with your doctor, be it telemedicine or in person within the past year the doctor has advised me (based on new lab results) without a more formal appointment. This is barring symptoms have not changed significantly since last being seen.
For a fast response you could try both calling and messaging. If that doesn't get their attention your Pharmacist may be able to help, as some have considerable experience contacting doctors offices and have mastered that art.

Even if your doctor is away for some reason another physician in their practice should be available to fill in for them. My understanding is your lowest TSH level will be obtained while lasting in the early morning (before you have taken any Synthroid for the day).

That is my best advise, run this by your doctor's office first if at all possible. Do they have a Same Day Clinic attached to their practice? Or even does your healthcare plan allow you to be seen by Doc In the Box? Someone with a license behind their name is your best bet, and I don't have one!