The short answer: YES. At least while you're just starting out.
Unfortunately, this happens to everybody that plays. The good news is that because your fingers are hurting, you're doing something right. If your fingers didn't hurt, you're not pressing down hard enough. Your fingers aren't used to doing this type of manual labor, so simply pressing down the strings is hard enough at first, but on top of that, you will find that the skin on the tip of your fingers is quite delicate. Pressing against a tough string will naturally cause them to hurt. In fact you might even see impressions where the strings were on your finger tips. Like the old saying: no pain; no gain!
Your fingers will soon develop calluses (dead skin getting thicker) if you practice correctly. These calluses will keep your fingers from hurting in the future. You NEED to be consistent with your practicing to develop them though. So, practice every day (even if it's 20 minutes) for 2 weeks. It is very important to be consistent in this. If you take a few days off, you will be starting from scratch. For now, make sure you are practicing every single day. Also, remember you actually want to feel a little pain. If you feel no pain, you're not practicing correctly.
You should be good to go at that point. From there, you will have them for life as long as you play every once in a while. It takes about 2 weeks to completely loose them, and then you're back at square 1. I found this out after I took a 2 week rest from guitar. Your fingers constantly produce new skin cells, so your current calluses only last so long. Once you loose them, you gotta get them back! Not fun.
So, for now, just practice until they are a little sore, and in about 1 to 2 weeks time, you too will have calluses and can join the ranks of the pain-free players!
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