How to prevent allergies while traveling?

I once visited my sister for a week (she has a cat and I'm allergic) and this is how I coped.

Started on daily zyrtec before I went there. (you can take at night if it makes you sleepy)

Started using Nasocrom everyday before I went there and while i was there. (good OTC allergy nosespray)

Did nasal rinses twice a day while there.

Keep benedryl on hand and took it every 6 hours while I was there

She treated her carpets and couches with frebreeze allergen reducer the day before I arrived. You might see if your friend can do this or will do it if you bring her some. Still, I avoided sitting on her couch if I could help it.

She ran an air purifier for me (but you could take your own and use it)

Rather than sleeping on her couch (only place available) I brought an air mattress to sleep on. If your friend is putting you in a spare room you could request that she wash all the bedding in hot water ahead of time, or bring your own bedding. Also keep the cat out of the room where you will be sleeping, if possible.

Wash hands often to prevent transferring dander from your hands to your eyes/face

Talk to your family doctor. Tell him the scenario and he can prescribe you something.