Is it still allergies if you have a cough along with the runny nose, congestion and itchy eyes?

Allergies and Cough: It very well could be if it is related to post-nasal drainage causing the cough. But allergies and asthma are strongly correlated so it could be a cough-variant asthma or the basic form of asthma. It could also be due to reflux since this can trigger cough. And sometimes it is due to a different medication. Start by controlling the allergies and work your way down the list.

Yes: You can have coughing if you have post-nasal drip as a result of allergy.