Is corticosteroids (cortison) is the solution for allergic asthma patients?

Usually. Inhaled corticosteorids are the cornerstone to treat persistent asthma. Very liittle is absorbed into your body. It works locally in the lungs to reduce inflammation. Allergic reactions cause inflammation so to answer your question- yes.
No. Cortisone can help a patient with allergic asthma who is having a flare, but it has many more side-effects than the medicines that are now used for asthma treatment and control. Asthma medicines are usually inhaled and are classed as rescue medicines (help get rid of symptoms quickly) and controllers (which prevent asthma symptoms and make the disease less severe). Talk to your doctor.