Persistant cough from allergies. Can it lead to something more serious. Coughing to where puke comes up my throat?

Inflammation. A chronic persistent cough may be due to bronchospasm so you may need an inhaled steroid inhaler as well as a bronchodilator to control this cough. It could also be due to allergic post-nasal drip which may need a nasal spray to control. You should be evaluated by your doctor so the cough can be diagnosed and treated.
Your coughs. Coughing by itself is not a dangerous thing, but severe, persistent cough is not too comforting and may cause muscle strain, bleeding into eyes/nose, oropharynx etc...Yours sounds quite bothersome so why not have it checked out and treated? It maybe allergies, maybe asthma, or some thing else. Pertussis can make u cough really hard too. And contagious to others. So, consult your doc. Good luck.