I kind of slid into shopping "sideways." Before I really acknowledged my dressing to myself I had been married for some time. I would go shopping with my wife. She'd go to try something on and would sometimes leave her purse with me for safekeeping. This left me standing there with nothing to do. I'd amuse myself by shopping around for other items for her to try. (I wasn't buying anything for myself at that time) Often I'd find a gem that we had overlooked before.
So, I spent quite a lot of time in drab, shopping my way through the racks, with a purse slung over my shoulder and a couple of garments over my arm. If confronted, I had the perfect excuse, that I was waiting for my wife who would soon reappear. So, how many times was I confronted? Zero.
When I started shopping for myself I remembered that lesson. No anxiety required. Shop, find items I like, take to dressing room appropriate for my presentation, try on, reject, or buy.