There are a few possible reasons for what is going on with her.
First cats do not do well with change and while unlike dogs cats in the wild live solitary lives they can grieve when they loose their house mates or when someone moves out.
Even a small change can cause them to stop eating and develop behavior changes. THe not eating normally is a concern as when a cat stops eating or reduces the amount they eat the body begins to burn fat for energy. The problem with cats is that their liver can not process this fat and can result in a condition called Hepatic Lipidosis aka fatty liver. This can lead to liver failure.
While this could be stress related we also have to be concerned in a senior cat that this could be medical in nature. Senior cats are prone to problems such as diabetes, kidney disease and hyperthyroidism. Starting easily, sudden aggression and being more vocal then normal can also indicate a problem with the eye sight.
I would start with a vet visit for an exam, senior blood work to check for the problems I listed above and a good eye exam.
As for getting another pet that really is a hard call. I say that because this is something we see owners do often and in some cases it can help but in many cases it does not go well and the resident cat will turn the aggression on the new comer or stop eating all together, with cats we never know which way this will go.
As I stated above I would start with a vet visit first and then if she checks out ok then you could consider getting another cat but we do not want to do this if this is not something you really want to do. Perhaps you could talk to a local rescue and try fostering a senior kitty that needs a home and see how it goes. If you offer to foster then you would not be committed if things go bad. In some cases rescues will allow you to do a trial if not fostering and if things do not go well they will take the kitty back.
I would also like you to get some Feliway plug in ans even a pheromone collar. Both the plug in and the collar release cat calming pheromones that really help reduce anxiety and are very effective in cases like this. For the collars at our office we recommend the nuturecalm collar . Click here
I would also try to increase her play time if she is a cat that likes to play. just like with humans exercise helps to reduce anxiety. You can try things like a laser pointer or a fishing pole toy so she can not get close enough to bite if over stimulated.
I hope this helps and she calms down soon. Please reply back if you have additional questions or concerns and I will be more then happy to continue.