She really sounds like that could wear her out if she is doing the coughing and gaping all of the time. She might have some yellow plaques of infection inside her trachea or mucus that are making her cough so much.
Is she able to eat and drink enough with her constant coughing? If it is caused by a virus, antibiotics will not affect it. But, secondary bacterial infections can cause problems, and may be treated with AB’s.
If she is a welsummer, I would think that she would weigh more than 1 kg. You may want to get some Baytril to treat her for 5 days, or give her the max. dose of Tylan. I would give 0.2 ml per pound 3 times a day, or 0.3 ml per pound 2 times a day. And get a weight, either by using a kitchen scale or weigh her while you are on scales, and then subtract your own weight (which will be a rougher estimate, but maybe close enough.) Here is a thread about finding Baytril, and dosage is in post 3:
https://www.backyardchickens.com/threads/baytril-enrofloxacin-sources.959119/
Also, I just wanted to add that gapeworm can look like that, minus the other symptoms of nasal drainage, etc. Gapeworm is rare, but if you would like to treat her for it, you could get SafeGuard or Panacur Horse Paste, and give her 1/4 ml per pound orally for 5 straight days.