I removed a mole on middle finger today
The laser therapy didn’t hurt me but the numbing shot before surgery hurt.
I have heard a mole on a palm is bad in fortune telling.
And the mole appeared suddenly one year ago.
When I was doing something , I had thought Did I mark here by a pen inadvertently ? It had been bothering me.
So, I had wanted to remove it.

Does it sound natural?

See a translation

I removed a mole on middle finger today.

(We usually say I _had_ a mole removed from _my_ middle finger. This means someone else did it, not you. If you removed the mole yourself you said this correctly.)

The laser therapy didn’t hurt but the numbing shot before surgery did.

(We don't have to say "me" because we already know you are talking about yourself from the last sentence. Since you just said "hurt" earlier in the sentence we usually assume the word hurt later in the sentence without repeating it.)

I have heard a mole on a palm is bad in fortune telling.

It appeared suddenly one year ago when I was doing something.

(It is unnecessary to say "the mole" again because we know from the last sentence the mole is what you are talking about.)

I had wondered, "Did I mark here by a pen inadvertently?" The mole had been bothering me.

(Here you have to say "the mole" again because the last sentence was about the pen. If you don't say "the mole" here we are not sure if you are talking about the pen or the mole.)

So, I had wanted to have it removed.

("So I wanted to remove it" means you will remove it yourself without the help of a doctor.)