This is the difference between "active" and "passive" verbs.
An active verb is when the subject does something. This is the more common form, and probably what you are used to as the "normal" form.
A passive verb is when the subject is the target of the action. Usually we indicate a passive with "is" or "was" plus a past participle of the verb.
Active: Al gave the box to Bob.
Al is the subject. Al did the giving.
Passive: Al was given the box by Bob.
Al is the subject, but Al is not doing the giving, he is doing the receiving.
Sometimes people use "got" rather than "is/are". We could debate whether this is grammatically wrong, but it's surely informal.
So more formal: Al was fired by his boss.
Informal: Al got fired by his boss.
If we said, "Al fired Bob", that would mean that Al was doing the firing, and Bob was the person who was fired. "Al was fired by Bob" or "Al got fired by Bob" means Bob was doing the firing and Al was the person who was fired.
So to get to your example: Blushing is something that you do, not something that is done to you. So the correct phrasing is, "I blushed when she looked at me."
You might Google/Bing "passive verbs" for more information.