I pumped "Full-Time" for over a year (only nursed at night), so understand what you are going through.
Is it your breast that is hurting, or the nipples? (or both).
If it is the breast, then it sounds like you are not getting all the milk out, or maybe you have a clogged duct. Be sure to pump until they are empty. I pumped just one side at a time, and massaged (ok, it was really squeezed) my breast to ensure all the ducts were emptied. As a point of reference, one side took me about 25-30 minutes (with electric pump), and I produced/pumped between 5 to 8 ounces of milk every 4 hours. After you pump, your breasts should feel better, and when you feel that "pressure" again, just pump again.
If it is your nipples that are hurting, then it may be your shield is too small. Having a shield too small will cause irritation as they are "sucked" into the cylinder, and make your nipples feel like they are chapped. If this is the case, you can buy larger sized shields. Check with your manufacturer for their sizing options. If you have a Medela, they have a helpful informational line where you can speak to someone who can give you advise on the correct size for you.
Good luck! The first few weeks are the hardest, since your body is trying to figure out how much milk to produce for your hungry little one.