It sounds like a severe eye infection from an injury like a blow or tear. Do not force open the eye, but rinse it gently with warm water, try to keep the area clean and detect any obvious damage. The nose issue may point to sinus issues, but the eye's bleeding points to something much more serious. I will be honest, it sounds like your cat may have to lose that eye if it is truly that bad. Consult a vet immediately.
It could also be a tooth infection. Once my cat's entire left side of her head was swollen and when I took her to the vet, it was a septic tooth infection. The vet gave her meds and it was cleared up in 3 days.
Your cat could of gotten into a serious fight cutting the eye that's making it constantly bleed, My cat had a similar problem a bunch of teenages wacked my cat round the head with barbed wire and his head would stop bleeding and he also wouldn't eat. Take him to the vet to get antibiotics