Congratulations on your baby!
It is not normal for it to hurt or to have cracks like that, no. Definitely an attachment issue. The good news is that it is often easy to fix.
You need to see a good lactation consultant and have them observe you feeding. They should also examine your baby for tongue tie or any palate issues, just in case there's something else going on as well. It's not something you want to leave to chance as until you get the attachment right, your nipples will continue to be damaged and you'll quickly get to the point where you cannot feed - which is clearly not what you want!
You can call the ABA - 1800-686-2-686 - or PM Barb Glare to find an LC in your area (or can you see someone from the hospital?). They cost money, but they'll come to you and and help you fix this (and it's worth it - much cheaper than formula). Your local ABA group counsellors may also be able to see you (or perhaps you can get along to a meeting?) - they will be able to help with positioning and attachment.
It's really important to get real life help with this, and, as I said, it often is a very simple fix IF you get the right advice from the right person.

Good Luck!