If you start having an asthma attack and don't have your inhaler with you, sit upright, stop doing anything your doing at the time and sit upright right away, take long and deep breaths, stay calm and try drinking a warm caffeinated beverage such as a cup of coffee.
Seek emergency help if the asthma attack doesn't go away or just to be on the safe side go ahead and seek emergency medical help since that is the best solution for an asthma attack without an inhaler since having an asthma attack can be fatal if not treated.