Animal Dander and Allergy Shots

Hello, I'm new to the forum 🙂
I'm 38 and been asthmatic since I was 2 years old.
I take Ventolin and Beclometasone to manage it which works well for me. It only really causes me issues when I have a really bad cold/flu that goes to my chest or extreme physical exertion or around animal or bird feathers. That triggers my reaction, I fact the last thing I really remember when I had my first asthma attack before being taken to hospital in an ambulance was stroking a cat.
Recently I've also been diagnosed with allergic rhinitis... I'm told the two can go hand in hand. Lucky us. So I've been on antihistamine tablets for the last month.
So.... Main point now... my partners family have a dog... A hairy, continuously malting, just have to look at it and there's hair everywhere, Alsation.
We don't see them very often because they live about 400 miles away and he and I met just as the pandemic hit in 2020.
But anyway .... I spent last weekend with his family at my partners brothers house and the parents dog was there. I spent the whole weekend causing, feeling tight chested and a constant ache across my chest, and with the rhinitis side I felt bunged up most of the weekend too. And this wasn't even in their house.
So.... Chances are if I stay with them at their house, where the dog roams everywhere, I could feel even worse. So they want to find a "cure" or something that helps me to enable me to be in the house without feeling as I did or worse.
Antihistamines is something I've read on... But they didn't help this weekend, I've also read that you can get allergy shots. You have a load of allergy tests done and then you get shots of whatever it is that "upsets" you to build up your system against it.
Has anyone ever done this?
Has it helped?
Do you see you GP about this?
Any other advice?