congratulations on your new baby. i'm not a bfing expert, i'm sure one will be along soon (maybe tomorrow, this is a UK site so most activity is daytime/evening GMT) but i can give you some thoughts in the absence of anyone else.
have you been able to contact a bfing counsellor to get them to look at your latch? that's really the best help to get, in my experience paeds and doctors are awfully quick to recommend formula, whereas a BFC can actually help you to keep bfing exclusively. if you are in the UK i can really recommend goiing to www.howbreastfeedingworks.com as all of the relevant numbers are on the front page.
have you heard of lansinoh? gosh, it's good stuff. get it tomorrow, it'll help your poor nips. i think it's about £11 and i remember buying it in mothercare in the UK. but i'm sure you can get it all over.
in the meantime, fresh air and breastmilk gently put onto the sore nipples will be the best thing to help them heal.
i introduced a bottle at about 5 days (on advice of, you guessed it, paeds) and i did regret it becuase the expressing etc affected my supply, but it's not a one-size-fits-all thing, your supply might be fine. (mine was a bit rubbish, tbh). it's maybe not a course of action i'd take until i'd had a live human BFC had looked at my latch, though. do you think you can stick it out a bit longer?
this happened to my friend, by the way, and her docs pointed out that until very recently the baby was swimming around in all manner of her bodily fluids so a bit of blood wasn't goiing to be the end of him. but it's what you feel comfortable with, obviously.
as i say, congratulations, remember that bfing is a co-operative process so both of you are getting a crash course right now. you don't have to decide immediately if you think you can stick out the bfing with the sore nips.
oh, and nipple shields too. not something i know a jot about but worth a try if you're thinking about going onto formula directly, perhaps? some people don't like them, tbh (i'm not actually sure why but i'm sure it's relevant) but imo better to try them before the formula thing.
and hey, if you give it your best shot and end off mix feeding or ffing, there are worst things. it's what i did. it's important, but it's not the sum of you as a mother. but it's nice to know you've really tried and had good information and support, isn't it? good luck.