He probably is acting like he is hungry because he is... LOTS of times, with breastfeeding, a baby "cluster feeds"...meaning, they nurse even every hour. This is normal and common. You must feed him whenever he is hungry, no matter how often.
ALWAYS feed on demand. Always... and your body should produce milk according to your baby's needs.
Breastfeeding is arduous and takes time.
But also VERY important is:
1) Make SURE your baby is latching on properly...the ENTIRE areola should be in his mouth encircling it. He should not just be sucking at the tip of the nipple... this is not proper latching on.
2) to get full and proper benefits of breastmilk nutrition... a baby must nurse long enough to get to the "hind milk", which is the denser richer and nutritionally denser part of breastmilk. To get to the "hind milk" it takes about 15 minutes of nursing. MANY babies, nurse for at least 1/2 hour or more. Or if they are a power-nurser maybe less.
3) I would nurse using BOTH breasts PER session. That way....there is not a long period of inactivity for each breast.. .and thus, they will produce more milk, on demand.
For example: if a baby nurses on the left breast, then say in 2 hours later on the right breast... then in 2 hours later back on the left breast...then that is 4 hours that the left breast was "idle" and was last nursed on...to me, that is awhile. With me, and per my Doctor, I nursed with BOTH breasts per session. To me, this helps with milk production. I did this with both my kids, and my milk production was good.
4) yes, push through the "pain." It will get better, your nipples are just getting used to the nursing. But look out for any infections, if that applies to you. Use Lanolin breast creams, which helps a great deal. ALSO, when bathing, do NOT put soap on your breasts/nipples, because this dries the skin out and makes it worse. Just wash your breasts with warm water.
Your breasts will heal. This is the nature of breastfeeding.
(5) Don't use formula... unless you know FOR SURE that you are not producing enough milk. If you use formula... then it will impact your milk production, lessening it.
IF your baby is growing/gaining weight well at each well-baby check-up...then your milk supply should be enough.
But remember, NURSE ON DEMAND, 24/7. No matter what.
all the best, hope this helps,
Susan