Learning from your mistakes is the bedrock of learning. If you are learning something new you will make mistakes. Figure out why you made a particular mistake, and you will learn more from it than you would have if you had gotten the correct answer.
Don't fear to make mistakes. The harder your studies, the more mistakes you will probably make, because you are pushing the envelope harder, and learning more. If you are doing original research, mistakes are even more important. If you are doing original reseach and are not making mistakes, you are deluding yourself, either about not making mistakes or about the originality of your research.
You can learn more from mistakes - from things that go wrong - than from successes. Success can always be the result of accident or coincidence, things outside of your control. Sort of how it's easy to make money off the stock market when most stocks are going up or in an occasional year; but making money from stocks consistently (as a result of your knowledge and intent) is far harder and less common. Some people claim it is effectively impossible to beat the market index, that those with good long term results are mostly just luckier than others.
Since you are trying to succeed, however, a mistake is a definite sign that something in your knowledge of the situation or in your technique needs refinement or even to be completely re-thought.
Learning from others is less painful than learning from your own mistakes, so you should learn that way whenever you can, but if you don't learn from the mistakes you do make, the pain will be for nothing, and worse you may make the same mistake with same pain again.
"Experience is a dear teacher, but fools will learn from no other"
-- Benjamin Franklin.
This doesn't mean that learning from experience is the sign of a fool, rather that experience is the only way a fool learns. Everyone learns from experience.
"The study of history offers that opportunity [to learn from others experience] in the widest possible measure. It is universal experience - infinitely longer, wider, and more varied than any individual's experience." - B H Liddell Hart, Why Don't We Learn from History?.
The same is true of all of the sciences and engineering where the body of knowledge is accumulative.
"While one person hesitates because he feels inferior, the other is busy making mistakes and becoming superior."
-- Henry C Link
Don't fear mistakes, use them.