How often do you get a dose change in Levothyroxine? Should I go to an endocrinologist?

I've been diagnosed with Hypothyroidism since 2006/2007-ish when I was 13 or 14. My dose stayed pretty consistent, and, for most of that time, I really felt great and had no issues with it.

3 years ago I moved to a different city and have a new primary care doctor. My dosage began lowering and since then I have consistently varied between 100mcg and 137mcg, but have not had a consistent dose for more than three months (until now). This I feel was taking a toll on me physically as I struggled to gain weight, had pretty bad stomach/bowel trouble, and was sleeping more (usually 8-10 hours a night, which is more than I needed in the past).

I've been at 100mcg for the last 6 months and have been feeling great. The issues described above for the most part completely went away. I felt my levels were stabilizing.

However, my last blood work came in and my TSH was 6.43. I have a follow-up with my primary care doctor and expect them to change my dosage (again). I'm worried this whole cycle is going to rinse and repeat.

I feel like this is taking longer than it should to get me to a consistent dosage. Should I ask to be recommended to an endocrinologist? What advice would you give for my situation?