I started taking piano lessons when I was 8 for about 10 years, but quit for 8 years for college (shouldn't have done that!), but I have recently started to regain interest in the instrument and classical music and take up lessons again for just a couple of months.

Anyway, my fingers are indeed much slower than they were, so technique-wise that is a a problem. But a week ago, (after about a couple weeks of practicing scales/etudes/arpeggios etc...), my left hand started to feel pain, that practicing was a problem because my left hand was hurting, not the fingers themselves but the area towards the wrist. I had never had this before.
At first, I didn't think it was serious, so I tried to play through the pain (even after my piano teacher told me to take a break from the piano if the pain persists). But it got worse for the next 2-3 days, that I got quite worried, because my whole career depends on my 2 hands (well, especially the right hand, but...). Luckily, the pain all went away after those 2-3 days.

Has anyone experienced this? Does this mean my hands are now not used to playing and can get hurt if played too much? Can people really get their hands injured playing the piano, or playing the wrong way? How can we prevent this?

Less than a year ago I had an ulnar nerve entrapment in my left hand from playing the piano with poor hand position. I had to have a surgery and stop playing for 3 months after the surgery. It took the doctors a long time to diagnose it and I had to go through painful tests. Before my surgery it got so bad that I couldn't even tie my shoes! I had to go through 6 months of physical therapy and I just got done with that about 3 weeks ago. If you ever have pain in your hands that lasts for more than 10 minutes see a doctor immediatly!!!