OP, I don't have fat feet per se, but I do have large feet. Always have. My feet belong on someone 3+ inches taller than me. And this may be a long post - this topic hit a chord with me.
When I was in high school, I thought my feet were ugly because they were big. They were as large as my dad's (though he had smallish feet for a guy), which was horrifying to me at the time. My cousins teased me about it, people at school did too, and guys would put on my shoes and laugh at me when they fit; girls would go out of their way to show me their tiny, size 5-7 feet. I tried to hide my feet all the time. I would wear clunky shoes that hid any trace of my feet.
Then one day when shopping with my mom, I admired a pair of shoes that showed heels and toes. She said I should try them on, and I told her that people with feet like mine shouldn't wear shoes that show any skin (or shape). She was very confused and said that wasn't at all true.
Since then, I've come to love my feet. I've even had people tell me they have a lovely shape (which may be excessive, but still
I love shoe shopping now. I also have nice (if wide) ankles that I can show off. I wear shoes that show all manner of skin and don't give it a thought. It's a total 180 from how I was as a kid. There are still some styles of shoe that won't fit (pinches my feet) or aren't flattering on their shape. I avoid those. But there are a lot that look nice, too! It is hard to find my size sometimes, but often a last pair will be in my size, so I get a discount!
, your feet are probably a lot more awesome than you think. I'd take a good friend or a family member you like and go shoe shopping with them. They'll help give you a perspective outside of the (probably erroneous) one you have about your feet. I bet you they're lovlier than you think.
Now if a guy puts on my shoes and jokes about them fitting, I tease back that I have a nice dress that go with the shoes if he'd like to try it on, too. That usually shuts them up or makes them laugh with me.
I feel almost zero insecurity about my feet now. The only major bummer is that I can't share shoes with friends or family. But they also get bummed that they can't wear my cute shoes either, so it's pretty even.