Laura, I have been researching the Thomerson name in the UK for some years and have established a one-name-study under the Society of Genealogists here in the UK. My records go back to the 18th century to Essex, when the name was Thomason - I have not yet tried to go back futher. Most of the family later lived in East London and there are a few that still do.
I am aware of only one Thomerson who emigrated in your direction - he was Orlando Thomerson who emigrated to Canada and I then "lost" him.
I have tried on one or two occasions to contact Thomersons in the USA and have had very limited success - perhaps folk think I'm selling something and don't want to reply!
I can export my Thomerson data in GEDCOM format, or other formats as might be suitable. Let me know, I'll be happy to send it.
As ever, there's no such thing as a free lunch!! so do you have any information that might help me. I would be very interested in whatever you might have; any Thomerson records whether linked into a tree or isolated.
Please email me on email@example.com and hopefully, I will be able to answer your interests in Thomersons in England.