Getting hurt while riding a skateboard is normal. It might not be too comforting to know that a lot of people get injured when skateboarding; still we can say that it's part of learning the sport. However, your fear of getting hurt is yours to solve and you cannot blame the sport or other people if you happen to get cuts, bruises or broken bones while skateboarding. The thing is, you need to overcome it. But how?
Overcome fear by getting enough confidence. The best way to do this is to pad up, seriously. Wear a helmet, knee pads, elbow pads, wrist guards, and gloves. You can also wear padded shorts if you want to. Don't worry if you look a bit ridiculous with these gears. As long as you are protected, you reduce the risk of getting hurt and you'll gain confidence.
Then, you have to practice. Start with the simplest trick. The ollie can be a good choice. Learning a trick or two will allow you to gain confidence. It may take you a few months or even years to learn just one trick so stay focused with your goal. A lot of newbie skaters give up skateboarding because they either get hurt or never learned a trick. Keep your interest high and fear will be a thing of the past.
You also have to ride with your friends. Riding alone in full battle gear will make you look like the mascot. I did not tell you not to gear up properly. What I mean is go out and make friends if you don't have any. Skateboarding should be fun. And although you cannot invite someone to ride with you on your skateboard, you can ride along with friends who don't ridicule you if you don't know how to do a single trick.
Finally, you just need to get hurt. But don't remove your gears. If you are padded up and you fall, it might not break any bones but you will get hurt a little. And when you do, your body learns how not to do it again. You gain confidence and overcome fear.
Accept this: skateboarding is a painful sport. Even pro skaters break a bone or two once in awhile. You will get hurt but if you ride with care, you can skate another day and improve your skills.