Allergy?

I notice that whenever my kitty goes out into my AZ room her nose from the bridge to the tip gets something like looks like a rash.  red spots. Sometimes they Bleed.  I first though she was getting into fights with my other kitty but found this is not the case.  She loves to go out there where I have plants that she like to hide in.  I have tried putting peroxide on and emu oil but she hates anything being put on it.  She is just fine if she stays indoors but she just loves to be out there.  I also have a pet door so she can go out whenever she wants as that is where the litter box is located.  I know the best solution would be not to allow her out but she loves it so much.  Since I am on SSA it is difficult for me to take her to vet as I can't even afford my medical treatments.  Also still paying off large vet bill for teeth cleaning for my oldest kitty. If this is what I am thinking an allergy can I give her some childrens allergy meds?  I used to do that for my dog and it helped him.

I don't mean to sound ignorant, but I don't know what an AZ room is.

Also I don't know what types of plants you have, but some plants are toxic to cats. So be very certain that she isn't eating any of them. I would recommend keeping her from that room for at least a few days to see if it clears up or if it is unrelated to that area of your home.

Sorry I can't be of much help. Good luck tho

An AZ room is a patio which is enclosed with screen or similar materials. It is open to the fresh air and protected by either a roof or pergo or something similar. Mine has a roof with latice and sun shade material due to the hot AZ sun.
Yes, it does clear up whenever I can keep her indoors and that is why I am thinking it is an allergy. Either to the plants or possibly some little insects. She just loves to go out there and I hate keeping her inside all the time. Just hoping some other people have had same problem and know what I can do for her.