Bekah, i'd call vet now, i would.
this could even be worms crawling up his throat, or a bacterial infection, maybe something super easy to fix,

that delaying could
make worse.

Waiting another month is not a good idea, imo.
i'd skimp on everything else, even feed ol roy brand dog food if i had to, to be able to afford to get my coughing dog to the vet to see about the coughing, both YOU and the dog will feel better. I Hope so much all is well and soon!!!
I know, Bekah, at your house, you are only a teen, and your parents are more in charge of vet appts than you are, so it's not entirely your decision, but, i hope you can try to convince your parents that your dog ought to be seen by the vet now. (without causing any family discord) It might be less expensive to treat it now, before it gets worse, (whatever it is..)
than it *might* be in another month.
It's also possible, the vet will have surgery room all set up,
and then CANCEL the dog's entire surgery, when he finds out the dog is sick. Most vets will try to avoid doing elective optional surgeries on dogs who are currently sick.
Please keep us posted..