Sorry about your hen with respiratory distress. Gapeworm is fairly rare, while respiratory diseases are much more common. There are viruses and several bacterial and fungal diseases that are common. What part of the world are you in? Is she able to eat and drink anything now? Can you get another pair of hands and look inside her throat with a light for any gunk, yellow patches, canker, or anything unusual? A vet is a food option if you have one familiar with chickens.
If you can get SafeGuard Liquid Goat Wormer (fenbendazole) at your feed store you can treat for gapeworms and other worms with 1/4 ml per pound given orally for 5 consecutive days.
Look for any nasal drainage, small bubbles in an eye or swelling around an eye, crackles or wheezing during breathing. There is not a lot that can be done for the gasping except to make sure she has good air circulation. Keep her warm and encourage her to drink plenty of water, and eat watery feed.