Urgent need to help me keeping my account safe

Hello,

I have a question. can any stranger enter my email address without knowing my email password?
I am a trading employee some customers told me that got msgs from an email address which is very similar with mine except one" i" before my email address characters.
actually this swindler`s name and family name is exactly the same as mine as no body suspected the forged text from him/her.
Now I am really worry , Although I changed my pass word and deleting the mark to sign in every time I want to enter my inbox I can see that the mark for saving my password is still there!!!!
If assume If this guy could enter my own email address would not bother himself to make another email so much like mine.
One of my customer embarrassed for the emails mistakenly sent to him claiming gor text to transfer money from my email address and the rest came from the wrong one. I think if she really got from my email she should have replied to my own email address not to the forged one.
Now I want to make sure if my own email address is safe. I changed my pass word bot i am worry about this person other forgery action.
Can I ask Internet police in Iran to sue him? would it be useful?
I should add here that I live in Iran.
Thank for your sincere help to reassure me.

rgs,
shiva
comm.dept.
zagros stone group co.