I used Tom's before cancer. it probably contains baking soda, which is good for oral care, but may not have fluoride. not sure. For Xerostomia, I use Biotene dry mouth products...toothpaste, Mouth wash, gel, spray, and gum. Their widely available where I live, but there are many other products known, which are mentioned on similar posts, so you can search. Other products may be harder to procure, maybe by mail order.
Another commercial product I use is ACT, dry mouth lozenges with xylitol, and OraMoist, a dry mouth patch, with xylitol and enzymes, which you stick to the roof of your mouth, and lasts for two hours. I tried it, and works.
I saw a brochure in my ENT's office called, Numoisyn, which come in liquids, and lozenges, which also increase salivary production, and viscosity. I have to see the speech and swallow therapist about it.
There are other ways to increase saliva, and discomfort. There are prescription meds to help like pilocarpine, cevamaline to increase saliva production. During radiation, some get Amifisone injection or infusion 30 minutes before to help protect the salivary glands. Carrying drinking water can offer temporary relief, using a humidifier at night. Drinking Lemon water, smelling lemons, sucking on stone fruit pits, hard citric candy, gum, preferably sugar free, helps increase saliva. Milk also replicates saliva, so that may be helpful. Even seeing, smelling food increases saliva production, and drooled over many dishes myself

I hope this helps, good luck.
Just realized this is an old post, but did add some new info.