There is technically no outstanding NHS bill so nothing to pay.
There is a difference between having no bill and having no debt. Just because you were not given a bill, doesn't mean there is nothing to pay and that you don't owe any money. The immigration rules use the word 'debt', not bill.
Basically, UK tax payers paid for the birth of your child, when they should not have had to. You should have been the one to pay for it, because you were not entitled to utilise UK tax payers money.
I’d have to have one generated which seems to me like a last ditch effort.
Last ditch effort? Getting a bill should be top priority in a situation like this.
Your situation is no different to anyone else's, and paying for your treatment is a requirement. Many visitors to the UK use the NHS every day and they all have to pay for their treatment (even if they don't get a bill at first)... why should you be a special case?
If it was just a couple GP visits, no problem but it was an emergency delivery. Where does my care end and my daughters begin?
For you, any immediate emergency treatment in A&E is free. Any treatment outside of A&E is not free.
For example, if you were in a car accident and were taken to A&E, your ambulance and immediate care in A&E will be free, but as soon as you are transferred to a ward, or are discharged and seen as an outpatient, you have to pay for everything.
As your daughter is a UK citizen, all her treatment should be free, but any treatment you receive after the birth is not.
Most attorneys I spoke to knew less than I did about immigration so they are a last resort.
Hence the reason we don't recommend using a lawyer
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I guess my next question is what on earth do I do with my daughter. She’s British and I’m American. I had to buy a return ticket when leaving England because she is British. I’m sure it’s not a tough one to argue her overstaying in America...since I’m American, just another annoyance.
Actually, your daughter is also American. Providing you qualify to pass your citizenship to her (based on your US residency), she will have been a dual citizen since birth and is entitled to both UK and US passports.
Ideally, she should have obtained a US passport before you took her back to the US, as US citizens cannot enter the US on a foreign passport. It would have involved registering her birth abroad with the US Embassy and applying for her first US passport.
I would register her birth with the US government and get her a US passport while you are waiting for your visa to be processed.