Hmm. I’m not a professional - and I think this is a great question for any/all of the care providers you mentioned - but my first instinct is that thoughts you’re having (“This is awful. She could start to go downhill ANY SECOND. Maybe I should just sell her so that I don’t have to watch.”) are not about the horse herself. You’re having this anxious/depressed/what have you thought pattern and it’s latching onto your horse, and the barn in general, because she’s important to you.
To answer your unasked question, no, I don’t think that selling your mare will make you feel better. Your unhappy feelings and thoughts will just latch onto something and some place else, and you won’t have the commitment of your horse to get you out of the house. (I’m projecting on that last bit - that may not be an issue for you!)
You mentioned getting a younger horse, but since your mare is only thirteen, I wonder whether you’re not getting as much out of riding her as you used to. If she’s not the right horse for your riding goals, but you don’t have the finances to support two or even just purchase another horse, then would it be helpful to think a bit about what you want to get out of having a horse? There are so many wonderful benefits to having your own horse: having something to call your own, the pride of successfully caring for another creature, the smell of their breath, the satisfaction of watching them eat hay, scratching their itchy spots or giving them a good bath…and just like any relationship, your shared history (you two have a lot of that!) has huge value. We joke a lot about the PITA parts of horse ownership, but we do it for a reason.
The part of what you described that isn’t necessarily irrational is the fear of watching someone or something you love suffer or die. It’s very painful, and horses don’t live as long as we do. It hurts to watch them go, especially as their care-takers, and I don’t think it’s wrong to be afraid or worry about that. This fear and worry is what keeps us all honest in scheduling our vet and farrier appointments!
To share my story, I moved about a year ago and have really struggled with anxiety/depression ever since. I just didn’t adjust well at all. Before, I lived in a small city near all of my closest friends, and I worked at a fun job in a small office with coworkers I picked out myself and really liked. Then I moved to this much bigger city where I knew no one but my SO, and worked from home in a job that was brand new to the company. It was really hard to meet new people, establish my own routines apart from my SO’s, or even get out of the house. My mind turned into a sieve, I had no idea who I was, and I just felt generally awful. I thought I was losing my mind! Eventually, I talked to one of my neighbors, and we came up with a mutually agreeable plan: she was getting a puppy but was worried about leaving him alone, whereas I was really suffering for company during the day and routine. Viola! And of course, I had help.
By contrast, when I sent my horse to a retirement facility after doing self-care and co-ops for years, it was a tough adjustment too. After a honeymoon period, I really missed her! Especially watching her eat hay, and listening to her sigh. I ended up filling up the time with a second job. Ew!
It definitely made it hard to stay motivated about going to the barn, which was so sad, because like you, the barn has always been my happy place. Riding did help me to forget. Personally, what worked was to keep going through the motions until I could feel the fun of it again. YMMV, but you’ve got the bug and it doesn’t just go away