Don't worry about it. Liverpool is a very friendly city and has a lot of Irish people. You will not be hated or bullied because you are new.. You will find it easy to fit in and have friends within a week.
I'm not sure why you are asking for advice from Americans about Liverpool schools!
A lot of Liverpudlians have an Irish background so it might not be as different as you think - quite a good place to move if you're Irish, actually. You'll make friends soon enough and bullying is the same everywhere. We don't hate the Irish as the thousands of them here already know perfectly well - not least my sister's partner. The school will work out how to fit you in for studying for your GCSEs (the exams at 16).
No the British do not hate the Irish and many people living i Liverpool are of Irish descent with Irish surnames. The main problem for you is that educational standards in England are often much lower than in Ireland and therefore your parents should take great care in selecting a school for you
Make sure not to be rude to anyone there because students hate freshmen anyway, but don't worry you'll make friends. If you do get bullied you HAVE to tell an adult or someone trustworthy, and when you do get bullied, do not show them you're sad, because that's what they want. Don't give the bullies what they want, instead laugh and just tell them how funny they are and they'll see that there isn't any point in wasting time on you if you're not reacting.
Lots of Irish people in Liverpool your have no problems