Good evening, I'm Dr. Sara. I'm a licensed vet who works exclusively with dogs and cats. Thanks for sending in your question :)
I know that vet trips can be really traumatizing, but at an advanced age like 16, if they aren't feeling well I have to suggest a vet trip first off. There are so many possibilities as to what could be going on, and at an older age, some of them could potentially be life threatening or difficult to treat. I have seen many many cats lay in the litter box when they aren't feeling well - it's a pattern of behavior that I cannot explain. They do it in the hospital when they are sick too - even if I put a nice cushy bed right next to their litter box.
Definitely do keep an eye out for any straining to pass urine or feces. Urinary obstruction is quite uncommon in female cats, but possible. More likely would be constipation, which is a common issue with cats. You certainly could try offering her a little bit of canned pumpkin (about a teaspoon). It's unlikely to hurt but also might be helpful if she's mildly bound up. If it's more severe, though, she may need more intensive care like an enema and some IV fluid therapy. There aren't any over the counter enemas that I'd consider safe to use on a cat, especially one with an unknown health status.
If she's acting pretty normally but occasionally vomiting, that could be a dietary intolerance - as it sounds like you've had experience handling. http://www.petdiets.com is a great website where you can get a consultation with a board certified veterinary nutritionist to help you build your own nutritionally complete and balanced home made food for her.
Please let me know what she's up to and what other questions I can answer for you:)