My suggestion of formula isnt to make Tilly sleep for longer, it's to give you a small break and fingers crossed she will sleep after it, and as someone else said maybe it will let you see how hungry she actually is if she takes it. Please don't feel bad if you gave one formula feed, formula is nothing to be ashamed of! And you aren't giving up bf! You've done really well so far as I can imagine you feel like just banging your head against the wall. As I said, Logan had a bottle and it was totally fine and he was only 5weekz at that point. I fact, when he was 4days old he was admitted to hosp due to weight loss and was getting my boob and formula bottles top ups and again, I'm still feeding him just myself. When he went through a growth spurt at 5weeks he was really fussy on boob, would fall asleep at it then when I went to put him in cot scream until he was back on.
Sleep deprivation is one of the hardest things being a new mum brings. The other option is pestering your doctor to find out what might be making tilly so crabby.
Just do what you feel is right for you two, don't bother what anyone else thinks