that is occurring is not related to a problem with your stomach; rather it is something called post tussive emesis, which is a vomiting reaction to excessive coughing. In order to control this, you will need to get the cough under control, which in your case is going to require getting the seasonal allergies under control.
Seasonal allergies cause inflammation and swelling in the lining of the nasal passages, called allergic rhinitis. Allergic rhinitis leads to dripping of mucus in the back of the throat, which causes the cough. Treatment of the allergic rhinitis in a more effective way will lead to marked improvement in the cough. I suggest talking with your primary care doctor
to help you decide what treatment options are best for you.
Some cases of allergic rhinitis can be controlled with simply antihistamine medications like loratidine. However, many cases require nasal steroid sprays to get under good control or even other medications such as montelukast. Irrigation of the nasal passages with a saline solution, for example using the Nettipot or another commercial system, can also be helpful.
You should set up an appointment with your doctor to go over your symptoms and these various treatments.