You sound pretty normal to me. We come in all shapes and sizes. Is your labia REALLY that big or are you obsessing about something that, in the long run, doesn't matter? I'm sure your Labia looks like a lot of women's labias, and somehow they continue to lead happy lives and have healthy relationships. You even said you googled "enlarged labia" (i can only guess that their were quite a few porn links on there) and found pics of women with labias that look like yours! I second peekawho's statement. Your yeast infections should have nothing to do with the size of your labia. There are many different reasons you get them; from sex w/ a male or female that has one, diet, meds, tight pants or underwear, douching, etc. there's a whole bunch of posts on yeast infections here and I have never heard of anyone getting one because of their labia... We look in the mirror at ourselves everyday and we see what we don't like and think we need to fix it. Other people- they don't notice so much. They are nowhere near as critical. We are our own worst critic.
I doubt having labioplasty will help with your yeast infection problems.
You will have to research this with your insurance company, in regards for getting it covered. I would have no idea, I'm sure it just depends on the company, and on what your doctor is willing to swear is medical necessity.