I used to feel the exact same way. I used to get so nervous and embarrassed just walking through the cosmetics section at Walmart. But with time and experience I've gotten a lot more comfortable with it. I used to think that other customers and sales people would be looking at me and having the worst thoughts. But, my experience has been that 99% of the time, no one even pays the slightest attention to me. There has been the odd time that somebody has given me the 'stink-eye', but it's usually been an older woman, and it could very well be all in my head. I have really found that the younger ones, like 35 and younger, quite literally don't pay any attention whatsoever.
Also, I love going to some of the second-hand places. There is a huge one near me. I can pick up an armload of women's jeans and go to the change rooms and try them on. No body notices anything out of the ordinary because you just have an armload of jeans. I've even had a couple of mini-skirts mixed in with them before.
Shoes are a tough one. At least for me. Usually a size 10 women's will fit me. But, I picked a pair of 10w one time at a discount place. They were actually too wide and while they are great for posing and taking some pics, it is impossible to walk gracefully in them, because my heel just moves around too much. And just recently, I bought a pair of 10s, and they were good length-wise but the strappy part that went around above the toe area was just too small and I couldn't get my feet in them. I had to take them back, and the girl in the store, got all b****y with me... I'm sure she suspected that I had bought them for myself... But I don't know. I think some of the shoe places like Aldo, you can order shoes online and then if they don't work out you can return them to the nearest store, so that's what I'm going to try next.