Torino,
I was in hospital with my wee man for a few days as he had a urine infection, think he had a growth spurt as over a couple of days and he was not going longer than. Half hour off my boobs and at one point fed for 40mins a boob solid one after the other, I was absolutely exhausted (just can't sleep in a hospital, too noisy and getting disturbed with nurses) and began to feel unwell with flu. One of the nurses took him away to settle him and gave him a bottle of formula so I could rest and I slept for 4hours till he was ready for a feed again.
It's totally up to you if you wanted to give tilly formula, but in my case, it didn't do Logan any harm, my milk supply any harm, and it gave me some much needed sleep and if it was necessary, I'd do it again. I actually have two cartons of formula in house just incase I didn't have any expressed milk to hand to give him if I'm in that situation again.
Hope it gets better for you,a crying baby really wears you down