My dd and I both suffer with this, it is not pleasant in the slightest. Cold triggers the awful cough, as does getting a cold, virus ect.
The constant coughing sounds horrendous, leaves you with a very sore throat and tight chest, my dd is often sick due to the amount of coughing she does.
When the cough turns into something more serious like bronchitis or a chest infection I also get pain in my chest and have trouble breathing. My dd is only 4, and I've taken her to A&E numerous times due to her coughing - it keeps her awake at night and all day it's cough cough cough. It's awful to watch. She was diagnosed with likely asthma after demanding a hospital referal when she was 9 months old. I was diagnosed with asthma in my teens - suffered with chest infections, bronchitis as a child, but tbh I've not had to use an Inhailer in years and when I did it was when I had a cold, virus or bronchitis. I now only give dd her inhailers when she gets a cold, virus ect as I've realised the coughing only happens when she's a cold, virus ect.
As the op DD is in her teens, and otherwise feels well and isn't weasy or struggling to breath the op is probably ok waiting until later to get an Inhailer. Tbh the inhailers don't really do anything for my dd or I, they do help relieve the pain in the chest a bit but they don't do anything for the cough, the cough doesn't go until the virus or infection has gone. I've suffered from being a child, my DD unfortunatly looks like she'll be the same.
I think as the op dd is in her teens, and otherwise feels well, I'd also take the risk. However if she had other symptoms, weasing, struggling to breathe ect I'd be straight down to a&e.
Also a lesson learned op - please have an Inhailer to hand in future.
I'm no means a Dr, but do believe that 'most' mums/parents know when something is wrong that they need to seek urgent medical advice.
The thing that has annoyed me most about your question op, is that cost is a major factor to you seeking medical help for your DD, and that because we (the UK) have the nhs system where we can obtain help. For this, I'm afraid you'll be well and truely slated. If you'd have mentioned your DD's symtoms - most people I assume would say yanbu!