You have two potential hurdles...
1. You will need a pilot medical certificate from the country where your airline is based.
2. Some airlines have their own additional medical standards, and even do their own medical exams. This is common in Europe and Asia, less so in the US.
No one here can really answer your question...it depends on where you plan to fly, what their rules are, and the severity of the condition. Also, asthma may improve as you get older.
I suspect in most places, the need to carry an inhaler might disqualify you from airline flying. The US is probably more lenient than most other places, and many US airlines do not require a medical exam other than the one the government (FAA) does. So if you can get an unrestricted US FAA first class medical, you could have an airline career, although you might not be able to get hired at all US airlines.
When you get old enough to need to make school/career decisions you should probably find a private aviation medical consultant (in the country you wish to fly in) and get some professional advice. Do this the BEFORE you take any government medical exam.
This website might have more european info: pprune.org
Good Luck