Do you know of any ways of getting rid of wheezing without an asthma inhaler?

Yes.: Leukotriene receptor antagonists, like singulair, are asthma controller medications that you swallow. Albuterol, the most common bronchodilator, is available as a liquid and as tablets. Controller Budesonide (pulmicort), and bronchodilators albuterol & xopenex (levalbuterol) may be administered as an aerosol mist by nebulizer. For some these are easier to use than inhalers. Avoid cigarette smoke.

Yes: The mainstay of asthma treatment, and the main reason to get an allergist involved, is to identify the allergens that trigger your wheezing and let your allergist educate you about how to reduce your exposure to these allergens. The primary role of asthma inhalers is to reduce the lung inflammation that you can't control through allergen avoidance alone.

Depends...: Wheezing can have many etiologies, the most common one being bronchospasm relieved with bronchodilator inhaler. Other possible etiologies include gerd (treated with anti reflux meds), sinusitis (treated with nasal meds), foreign body (treated by removal of foreign body), etc. So, treatment of wheezing depends on cause.