Hi @Susie,
You will want someone who is familiar with ES, this article i posted recently would be very helpful to give them if they are not:
Typical conservative care would possibly include very gentle soft tissue work and/or dry needling (may or may not be available in your state) to help lengthen and resolve trigger points in the muscles. This is parallel to treatment for Thoracic Outlet Syndrome (TOS) so if you can find a provider with experience there and then add the ES education that would be helpful as well.
I do know of a few people who are looking into surgical thinning of the omohyoid muscle by a vascular surgeon. This is of course a last resort when all other conservative care fails.
Sometimes the process of C1 (the first cervical vertebrae) can be pressing on the jugular as well as the styloid. This can make things a bit more complicated but that process can be shaved down to mitigate this if it is present.
Hope this is helpful! Sending you every good!