Why are they making me feel badly?

My heart goes out to you. When you wrote "She ran away. Again" that did it for me. Especially the "again" part. Pick the best place possible with a clear conscience. Mom needs to be somewhere safe. Here comes a hug from me. Put on those big girl panties (I'm assuming you're a girl) and get going. You can do this.

It sounds like they are being very self serving in their advice, after all if you place your mom they will lose you as clients.
It is true that many nursing home residents are on medications to improve their mood or decrease anxiety, but then many elders in the home are on those meds too. The trick is to find someone who will work with you to find a balance of the right meds for your mom. Being afraid, panicking over minor issues, being aggressive etc is not conducive to a good quality of life, but it shouldn't be necessary to drug her into a stupor either. Proper medication just might be able to give a little of your mom back to you.

Mica, I don't mean to sound cold, but nobody can make you feel anything without your permission. You need to trust your own judgment and listen to your own reasoning, and let people say what they will. Lots of people think sending elderly to nursing homes is a bad idea. I think home health care workers probably err in that direction because their livelihood depends on keeping seniors in their homes. So what?

You can't take care of your mother at home, even with 24/7 help. You believe a nursing home is your best and maybe only option. Don't pay attention to anyone else. They're not in your position. They all have their own agenda. Just press the "ignore" button and carry on.