I don't have any suggestions relative to the cost associated with medical care (sorry). But I do think it is important for you to find care - and the right care. There are thousands of hematologists out there, but MPNs (of which ET is one) is so rare that many hematologists just are not knowledgeable in this field. And if you are going to get to the bottom of your diagnosis and get on the right course of treatment, I would urge you to start with a known expert. The following website has some good information and a list of proven doctors.
https://mpncancerconnection.org/2017/12/what-is-an-mpn-specialist/
Also, you mention that you are in TX, and it is my understanding that MD Anderson has extensive expertise in MPNs. A link to their website:
https://www.mdanderson.org/cancer-types/myeloproliferative-neoplasm.html
And here is one more website with some helpful questions to ask your doctor.
https://www.mpnresearchfoundation.org/find-a-hematologist/
Certainly worth it to visit with a specialist and get initial bloodwork and genetic testing. A BMB can be pricey, but may be able to be deferred (I didn't have one for several years after diagnosis myself). As others have pointed out, some of the treatment is low cost. The risk of not doing so can be life threatening (e.g., clot, stroke).

The good news is that if you do get a confirmed diagnosis of ET, it can be easily manageable. Many people live for years/decades with few or no symptoms. Best of luck to you. Hugs