Answer:
I start with an E end with an E and have a letter in me.
I'm really blue but when you see me I'm red. You don't see me too often. I'm there for you if you're hurt.
I get wet when drying. I get dirty when wiping.
I am a kind of coat that can only be put on when wet.
I tremble at each breath of air and yet can heaviest burdens bear.
What do you purposefully put lots of in and on your body, but run away from when you encounter it outside?