Hello, and welcome.
I'm sorry you're worried about your boy's strange symptoms.
From your description, it sounds like he may be starting an upper respiratory infection, he may have a painful, swollen throat, as in tonsillitis or something related to a kitty cold, or he might be experiencing a respiratory problem. When a cat stretches his neck out the way you describe, it usually means he's not taking in enough oxygen. He could have pneumonia, bronchitis, asthma or the strange sound you heard could be a 'reverse sneeze.'
The licking of his lips and swallowing hard are signs of nausea. He may have excess stomach acid or acid reflux, and stomach acid is coming up into his throat and burning it.
Because he hasn't been eating and is lethargic since these symptoms began, it would be advisable to have him evaluated in person by his vet, asap. Because it's late now, and a weekend, you might have to bring him to the nearest ER vet center, to get a definite diagnosis and treatment, so he's feeling more comfortable.
For the moment, if he's able to swallow a pill and/or drink water, you can give him 1/4 of a 10mg. Pepcid AC (Famotidine) tablet. It's coated and very small. It is an acid controller and should help with nausea. Here is more information:
If you can't get the pill down his throat, use a dropper to feed it to him in water. Crush the 1/4 of a pill with the back of a metal spoon and add it to water in the dropper, then feed it to him gradually, from the side of his mouth a little bit at a time. Wait for a swallow. You can rub his throat to encourage the swallow reflex. This might be difficult if his throat is bothering him, so instead of water, you can crush the pill and put it in a small amount of plain, jarred baby food chicken, containing NO onion or garlic. Beechnut Stage 1 chicken and chicken broth is a good one; then follow that with some more plain baby food. You can also water down the baby food and feed it with the dropper or a medicine syringe.
You can also run a humidifier in the rooms where he spends the most time, to help soothe his throat, until you can get him to the vet. I h ope you can get him seen very soon and all will be well with your furry boy!
Please let me know how he's doing and what the vet tells you. Thanks!
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