Thank you for giving Misty a home.
You can train her to go into a cat carrier, but it will take a few days to week or so. Get your carrier, open it and put a bed and some food in it, and just leave it in the house with the door open. Start with her food just inside the door, and when she starts to eat it, gradually move it farther to the back. Do not move the carrier; leave it in the same place.
If the carrier just sits there and becomes part of the household furniture, and that is where her food is, she will start going in and out of it. When you want to take her to the vet, leave her without food overnight, put the food in the carrier in the morning and when she goes in you just close the door. When you come back from the veteirnarian, do not put the carrier away; keep it out with the door open. She may be afraid of it for awhile, but most cats will start to use the carrier as a den or a bed if it is there all the time.
If she is a naturally fearful cat, there is not much you can do to change her basic personality. Someone may have kicked her and that is why she is fearful of you when you wear shoes. That may gradually improve with time, but if she learned to survive by hiding when she was young, it may not really change. You could try anti anxiety medication from your veterinarian and that might help.
Let me know if I can answer any other questions, and if this was helpful.