Hello Eve,
Congratulations on your new passport! If I was you I would want to use it right away. That would be so much fun to see that the border guard would just glance at it the way they do, and wave you through. Yes, you're most definitely a Transwoman now although you were one before of course.
Yes, we do have violence here in the US against all sorts of people. I don't know if it is more or less than in the UK but my intuition says it's about the same. One thing I'm rather sure of is that the "news" reports are typically negative. At least here, it seems like most news stories are about problems, complaints, crime. Otherwise it's not so interesting. And I suspect that the particularly heinous stories are the ones that make it into the press over in Europe and elsewhere.
Of course we do have laws against hate crimes such as battering someone because they are gay, trans, black, etc. and those crimes are prosecuted. We all agree that the violence toward trans people is especially scary. Clearly for some people seeing a trans person raises some weird emotion in them.
You also read about problems with sheriffs. Sure, some are jerks, corrupt, or worse. But 99.9% are excellent and here again we mostly hear about the bad ones. And generally as their badness becomes public they lose their jobs and sometimes have to go to jail themselves.
Hope this helps!
Emma