Cat keeps being sick after eating

My cat is about 11 or 12 yand she seems to eat her food and then bee sick later that night or through the night I have even tried cutting it down. But she just eats cat litter and then is sick again if she is not being sick she has diarheah. I took her to the vet a few weeks ago and the injections she got worked for a little while but never got told what was causing it. Even tried changing her food but it is still happening.

So she eats cat litter if there's no food down? That's unusual. Does she eat other inappropriate things? I'm thinking of pica where they can't help themselves from eating things they shouldn't.

She always has a supply of cat biscuits through the day and at night.. I also had to stop letting her out as the last time she was out she ate 2 or 3 really young mice whole. Ever since then she has been eating cat litter before being sick