US Citizen, UK Resident, Worked in US as Self employed

Have become very confused about whether I have to pay US Self-Employment tax or not. I did not earn any money in the UK this year, but I did earn money from a US company, working in the US, hired as a contractor.

I am unsure if this effects me, basically: newcomer link: https://www.ssa.gov/international/Agreement_Pamphlets/uk.html#certificate2 [nonactive]

Can I get a certificate considering I have never filed with HMRC before (I am a student)? If I can, then how do I fill out a Schedule SE form?

Would appreciate any advice!

Have become very confused about whether I have to pay US Self-Employment tax or not. I did not earn any money in the UK this year, but I did earn money from a US company, working in the US, hired as a contractor.

I am unsure if this effects me, basically: https://www.ssa.gov/international/Agreement_Pamphlets/uk.html#certificate2

Can I get a certificate considering I have never filed with HMRC before (I am a student)? If I can, then how do I fill out a Schedule SE form?

Would appreciate any advice!

How long were you working in the US and what did the work involve?