Welcome Anglefox32 and
How much longer is rain going to be an issue at your place? If only a day or two, get a bale of hay at the feed store and spread it on the wet ground. It should be deep enough the birds are walking on the straw, not in the water or muddy ground. It won't last more than several days but will hold you in a pinch. Is the rain blowing in one side of the run? If so, go to the dollar store and get a clear show curtain and hang it up on that side as best you can. That will at least give the run some time to start drying out.
Your chicken should not have a runny nose. That is worrisome. if it is a sickness you want to nip it in the bud before it spreads. Tell you what, take your birds health issue over to the emergency list.
https://www.backyardchickens.com/f/10/emergencies-diseases-injuries-and-cures
Title your post
newcomer needs help, sick chick?? We have a lot of folk there ready to help and they have seen all kinds of symptoms. Is the inside of the coop damp? Does the air smell at all like ammonia? If so, clean out the coop and fill it with about 4 inches of hardwood shavings. Not softwood. You can tell the difference because hardwood shavings smell like fresh dry sawdust. softwood shavings smell like turpentine. ask or poke a small hole in the bale and sniff. Try
Tractor Supply or your local feed store.
if you are at your feed store or
tractor Supply, ask of they carry Poultry Nutri-Dench. This is a great emergency nutritional supplement for any time birds are stressed as yours sound like they are now. It is different from other aids because it does
not need digesting Mainlines right into the bloodstream with 99% uptake in 30 minutes. I have used it on my birds for years and won't raise chicks without it. The 4 oz. bottle ( 6.99 to 9.99) is all you need, it's very concentrated. See this thread for usage instructions.
https://www.backyardchickens.com/t/746509/how-to-deal-with-travel-stress-in-baby-chicks
No, I am not saying your birds are going to die. I am just saying if your birds are stressed by sickness or environmental stressors, it often will inhibit how well they are able to uptake the nutrients in the food you give. So this product does not stress their G.I tract any more. It simply absorbs directly into the bloodstream giving the birds the extra energy they need to get past the stress. and energy to help get well.
Best Regards,
Karen and the Light Sussex in western PA. USA