Vet RX is like Vicks. It helps soothe a sick chicken. It's not a medicine, though, and has no healing value.
Here's how to handle your hen to look inside her mouth. Grab a big bath towel and gently but firmly wrap her securely in it so she can't flap, squirm or kick. Sometimes I wrap an ACE bandage around the towel to keep the chicken from working it loose.
Then bring one hand behind her head and work your finger into the side of her beak. This is the hardest part. Getting the beak open. You won't hurt her, and she'll wiggle her head like mad to get your hand off her head. But once you get a finger into her beak, then you can use the other hand to open her mouth all the way. Once you get it open, she won't snap it shut like an alligator. It should stay open with minimal pressure.
Have a flashlight handy to see well. If there isn't a nice hole at the center of her throat, but the tissue looks swollen closed, that's her problem. Or she could have crusty lesions in there. Or she could have a hair wrapped around her tongue and it's swelling her throat closed.
It absolute essential to look in her mouth.