"my raincoat" is correct and usable in written English.
For example: I hung my raincoat on the hook by the door before heading out into the downpour.
There would be cigarettes in my raincoat.
"I want my raincoat," Mickey said.
"You took my raincoat," Susan yelled.
"I want my raincoat," Mickey said, his voice rising.
I grabbed my raincoat off the floor, smoothed down my hair in the mirror, and went out.
Once indoors, I took off my shoes, hung my dripping raincoat in the wardrobe, and placed the bag with my texts and notebook on the top shelf because one glance at that and my mortification would return.
Seeing my friends, making new ones, and walking around Portland in my yellow raincoat while having a giggle attack.
I decided to patch a pair of ripped jeans and to replace a missing button on my favorite raincoat.
And that was the last Ronnie saw or heard of Flynn until the poor fellow was arrested a few weeks later on a string of charges that included, rather sadly, the theft of my Burberry raincoat from the house in Chalfont St. Peter.
Last Sunday, I put on my boots and raincoat, took my umbrella, and, as usual, went for a walk, in the drenching rain.
