You can pay charges as they occur and claim from Rutherford, UK prescription charges are deducted from the claim. Opening a bank account in the US is easy. Those nearest SLAC at the Sharon Heights shopping centre are Wells Fargo, Washington Mutual and Bank of America. For this they require the bank address, account number and wire routing number. It is worth investigating different ways of transferring money from UK banks to US banks.
Wiring is expensive and simply writing a UK cheque works.
If you decide to not open a US bank account, it is highly advisable that you get a good visa card, like a Barclay card. You can deal strictly in cash. There is no charge for cash advance on the Barclay card. This elimiates wire and bank transaction fees. Something to think about.