From Portugal to the UK, self-employed

[JustaWriter]

I'm a Portuguese citizen, currently living in Portugal. My girlfriend (Portuguese as well) is residing in the UK, working as an healthcare assistant and she's studying there to be a nurse.

We want to move in together, and we'd like to do so in the UK. I've been working as a freelance writer for quite some time now (my business activity is unregistered, though), and my plan would be to register as a sole trader in the UK and start paying my taxes there. My sole client is a US based publishing company.

Brexit and whatnot have me on my toes, though. I should move in with her before the 19th of March, right? Problem is, she's currently living in a hospital residency.

What should I even do? Try to apply for a National Insurance Number? Would one be granted to me? If so, would I be able to set myself up as a sole trader, keep on working with the US company, and pay my taxes in the UK?

It's probably a simple situation, but it has me terrified. I don't want her to move back to Portugal, as that would destroy her career, but I'm afraid I won't be able to move to the UK. Can someone, please, please, offer me some guidance? I've looked online and a read a lot, but I'm terribly confused about it all.