I used to be very sensitive and I still am to some extent.
I find it helps to really look inside when something upsets me and ask myself some questions.
What upset me?
Why did this upset me?
Do I really need to be upset over this?
Could I possible not be upset over this?
Is it possible I am overreacting a little?
Wouldn't is feel better to not be upset over this?

Breath in... Out... and try to let go.

It was hard at first and did not always work.
I found that the more I stick to it, the easier it becomes.
When you do this you are making a new habit, and changing they way your thought patterns work.

It might not be easy but it gets easier and before I knew it, things that bothered me before no longer bothered me.