Sup bro.
There are many 'short term' remedies such as rubbing your chest with Vix Vapor rub/deep heat, taking a hot bath, inhaling steam of a boiling pot of water, relaxing breathing techniques......
But I always reach a point where nothing seems to work anymore, I absolutely need to have a blue inhaler.....
You must understand that your g.f's asthma is being triggered by your surroundings. I'm guessing you guys live in a place surrounded by trees and quite possibly a river nearby. (My allergies go apeshit when there are pine trees around) When I lived in Perth, Western Australia (In the middle of the desert) my asthma was fine because of the dry climate. Asthma + humidity = Constant attacks.
There really isn't any cheap ways of doing this, In the end I would advise one of your loved ones back in England to send you the cash necessary to buy an inhaler. It's probably going to get worse once spring/summer arrives because of the pollen..... I never fuck around with asthma, there we're times when I thought I was a goner.... Sorry for the shitty answer.... But I speak from my own personal experience...... I hate asthma, I really do. I feel your pain.....
Good luck bro.