No. There is no transfer to the UK (although note that some info seems to be shared with Mexico and Canada).
The UK ONLY has a mutual recognition of driving points / disqualifications with Ireland.
They address this with regards to the future, hopefully initially with other EU states, which they don't even have this with currently:
We agree in principle that cooperation over disqualifications between
Member States other than with Ireland is desirable. Any EU Member
State may wish to enter into similar arrangements with us in the
future. At this stage we have no expectation of any other Member State
doing this. If they did we would need further Regulations in the UK
and, if changes in arrangements were contemplated, further public
consultation would be needed. The arrangements with Ireland will
provide us with practical experience in advance of possible future
approaches from other Member States.
tl;dr - your points are not transferred out of the US. However, within the US, if you apply for a new (different) state license, they'll check with your home (Texas) state and find out about any said points (source - attorney in Texas).
You can find your driving record through the Texas DPS Driving Record website (for a fee).
Crimal.lawyers.com have also researched this, and they've found that there are 3 national databases, including the NDR (National Driver Register) for basically blacklisted drivers.
If and when the US shares records, you don't want your name on this one. But from the same page, for now:
As our planet seems to grow smaller, the reach of the DLA stretches
father. The AAMVA is now pushing to have the DLA cover countries
beyond the US, Canada and Mexico