Coughing/hacking/gagging

Sulvek has been coughing as of late, sometimes once, other-times a few times but then she's done and goes right back to 60mph around the house. Just a little bit ago my sister witnessed Sulvek hacking. She stood up from where she was napping and sort of arched her back as she hacked then sat down with her head low (not crouching, sitting with her head down), then made a noise similar to a wet gag, followed by swallowing. The process repeated several times and my sister kept a close eye on her while it happened even putting a hand on her and petting gently, in which Sulvek began purring loudly in-between hacks. Once Sulvek started moving away she stopped hacking and coughing and walked out of the room like nothing happened.

Sulvek is a domestic shorthair, and has not had a hairball since we took her in. She was a stray for a period of time as a kitten but is now 100% an indoor cat. We can take her to the vet, plenty of money is saved up as of now, but my sister and I prefer others input instead of going straight to a vet.

If possible, get a video of it and take her and the video to the vet.  It could be anything from asthma to allergies or nasal drainage.