Does my cat need to see a vet?

Hi, I have two cats and dont know if one is sick, so I thought I should ask some "experts".

Possum is a grey and red short haired garden-variety type cat and for the last two days is sort of coughing/retching as though she had something stuck in her throat.

I thought maybe it was a furball? So anyway, I tried to convince her to eat some vegetable oil because I seem to remember hearing somewhere that was good for furballs. She didnt like her food with oil on, but eventually I gave her tuna in oil, and she did eat that.

But she is still coughing/retching, and I really don't know what to do. A vet is out of my budget unless there is no possible alternative so is there anyone wise who can give me some advice?

Is she sick and does she need a vet? Or should I be trying something else first.

Many thanks to all who read/reply.

There are hairball remedies you can buy, everything from treats to dry food treated with oils. Is Possum eating okay? Could she have an obstruction in her throat? Is she pawing at her mouth, have you looked inside her mouth to see if something might be there? I know of a cat who swallowed a thread and sewing needle, the needle got lodged in the cat's throat, till the vet took it out.

I know that vet visits are expensive, but most vets are so good about taking payments. If the coughing and retching continues, I would take the cat in for a look. Cats eat the darndest things sometimes.

This is the time of year that cats shed their summer coat to be replaced by their winter ones, if you groom Possum, that will help the issue as well (if it is indeed hairballs)