I'm worried about mom choking. Advice?

Swallowing problems are very individual and thickening or chin tilt or tuck are common but not universal answers. A swallow study by a really good dysphagia specialist who is more interested in their patients' well-being that covering his or her butt is the best bet. Even upright positioning may be more important or helpful for some people than others.

The other thing to distinguish is between risk of catastrophic choking such as big chunks of unchewed food that can require a Heimlich versus just getting a little bit down the wrong way that just is chronically bad for lung health. Also be aware that if there is no way to get enough liquids in by mouth on any given dysphagia plan, there is an option called the Frazier protocol that not everyone is aware of. Nasal feeding tubes or even G-tubes can be a great idea for some people, but generally are not that great for people whose swallowing problems stem from dementia.

Check with your local American Heart Association for a class in basic CPR. There is a method to do a Heimlich-type maneuver for a person lying down. It is used if the Heimlich fails for a person standing up and they pass out, you must put them on the floor and use this maneuver.

The swallow study, if done properly, is excellent. Here are some advice tips which you asked for:
1) Serve food that is palatable. No need for pureed food just yet. Perhaps in the future.
2) Always have a glass of liquid near by, preferably water, when eating.
3) Never let her eat white bread, doughnuts, croissants, danish pastries, even in tiny amounts unless you are standing by with the water. Somehow, these things seem to get stuck in the trachea. Don't worry about the windpipe unless she is taking in air, or talking while eating ( a no no ). This, of course, is the worst thing that can happen. Water will not help if food is trapped in the trachea. The Heimlich, and 911 should be called. Pray, that she can upchuck that piece of food. Choking is my worst nightmare, whether it be me or someone else. I witnessed a tracheotomy once, and it was all hands on deck until an airhole was cut open. Patient came alive after that, but was in need of serious attention by the medical staff.
Elderly people have to be watched.

If you do a search up in the "search site" bar (top right) and put in alzheimers + swallowing, you'll see a bunch of threads about this topic. If your mom is having trouble swallowing, you need to consider thickened foods and purees. My dad had a stroke and had a swallow study done and had trouble on one side (one vocal cord was paralyzed). So I had to get him thickened juices (nectars or specially thickened juices) to drink. He could still eat solids OK, but couldn't drink regular fluids or it would go down his windpipe. If something did go down his windpipe, he was to cough to try to get it back out. Not sure what stage your mom is in with her Alzheimers, whether she can understand that or not.

I'd have a talk with her doctor, who may recommend a therapist (maybe occupational, I'm not sure) who can guide you about the best foods to feed your mom and how to position her so that she has the best chance of avoiding choking.

I concur, have a swallow study done. So many factors are involved with an older person choking. The person may have structural damage ormay have forgotten how and when to swallow. My mother had choking problems. After much trial and error, surgery was the final option. It worked perfectly. Start with the swallow study.

Have the swallow study done. Perhaps liquid thickeners would help

I can't get my arms around her because she can't sit up without the support of a chair. If she is in a chair it is between us. Especially if it is a recliner which is where she spends most of her time. My mom won't respond to commands or suggestions. She is to the point where I don't even think she knows what I am asking of her. In general what do people do when something "goes down the wrong way"?

Does your Mom have Parkinson's? I tell Dad to tilt his chin up, that stops the coughing. I have Ms. It helps to do meditation deep breathing, if I can get on top of it, I can stop the coughing attack.

Why can't you get your arms around your Mom?

The first thing I can think of is to get a swallow study done, if you haven't already, because you sound very worried that your mom is going to choke. The people who do swallow studies then should be able to answer your questions and give you other helpful advice.