Op your baby is only a week old & wants to be close to her mummy. It took me a few months to realise this but babies do want their mummies a lot - for comfort & for food - & it's completely normal & natural for them to do so.
Also all (or at the very least, most) newborns have reflux to some degree as their stomachs are simply too immature. This is also normal.
As another poster has said, get yourself a sling & just carry her (I went to the loo, cooked, cleaned, walked, ironed with dd in a sling for the first few months). No you won't be making a rod for your own back by doing this. Babies want to be held, all completely natural.
Oh & you can put her down for 10 mins before she cries? You're lucky, mine screamed literally the second I put her down
. I remember it being a killer & then I stopped fighting it & just carried her in a sling.
I know you must feel utterly exhausted & unable to see the light atm but honestly it does get easier, I promise.
You're doing amazingly well, just hang in there.
But seriously - find yourself a bf support group, they are amazing 