My mom gets has trouble remembering people. She says she remembers her daughter, but then will tell me I'm an employee. Is this common?

First..,.
there is no "remorse" because what she says she believes.
People caring for people with dementia have to develop a suit of armor.
Ignore most of the comments because they are based in the reality of a person that has a brain that is not functioning.
Day to day you do what you can the best that you can.
No need to get nervous giving her meds. A medication to calm her also helps her, who wants to be anxious, fearful all the time.

My dad did this in the end stages of a degenerative brain disease. He would recognize my mother some days, and some days he would say ”where is the other lady who takes care of me? There was no one else.

There is no shame in saying the caregiving is becoming too much for you. Your situation sounds similar to mine in that the palliative care nurse said I was doing fine because they had no where to place my mom. If you live in New England you’re in the same boat. However, this does not mean you can’t move her into a skilled nursing facility if you need to.

Are you caring for her alone in your home now?

If you're giving her prescribed meds to calm her, there's no reason to feel nervous. They are medicines that she needs now that she's sick. You're doing her a favor by keeping her moods on an even keel so she can be the best she can be.

It seems to me that drugs have a bad rap now that we have so many addicts living among us. But drugs are a boon and a blessing for those who need them for medical reasons.

I'm a lifelong non-drinker, never smoked or used drugs of any kind. I don't even drink or eat anything with caffeine in it. I had family members who died of addiction. If there's anyone who should be opposed to any kind of drug, it should be me. Yet I have seen the wonders that drugs have worked in people who are close to me - pain meds properly taken for chronic pain, anti-anxiety meds for mom, antidepressives for friends, medicines for a chronic condition that I have.

We need to separate in our minds the good vs. the bad, and when our loved ones need help and the right drugs can help them, feel confident that we're doing the right thing.

You may now need to consider placement. This is very common in severe dementia. I am so sorry. If you cannot go on, time to speak with your own doctor and get documentation that you cannot continue in care you don't feel qualified to do. Ask palliative care RN to refer to social services for placement.