How long after worming can I give antibiotics?

[PoultryGirly]

Hi. I have a hen who had "cold" symptoms but I don't know what she has. A few months ago she got something like this. I then gave all of my chickens VetRX and she seemed to get better. About a month ago, though, she got her symptoms back again and I still gave the VetRX and she got better. Yesterday I noticed the symptoms again, but a little different. I gave them SafeGuard goat wormer (3.75 ml in a gallon of drinking water) yesterday because I thought she had gapeworm, but now I'm not sure what they have. The wormer I'm supposed to give 3 days (today is day 2) and not eat the eggs until 14 days after the last dose. I also just read that VetRX doesn't CURE the cold, it just relieves the symptoms, so I think that's why she keeps getting it. Her symptoms are: shaking her head while sneezing, a really high-pitched hiccup, and you can hear her breathing. Otherwise, she eats like a hog, drinks, and her egg production is high. I want to give my hens antibiotics to cure this, so I got soluble Duramcin today. How long after this worming should I give them the Duramycin? Thanks so, so much!
BTW, none of my other chickens have these symptoms.