I was in same situation like yours when i graduated from uni. but never give up. I graduated from aviation management department at uni and was looking for job around 6-7 months i've applied many companies in istanbul but i didnt get any respond from many of them. So i got job in represantation company with my friend's help(he was working for that company) and its been 1,5 year im working here started as an supervisor of airline and became OCC now.
My opinion from airport experience apply for handling companies like swissport etc. if you can get job as an traffic agent or ops agent it is going to be great experience for you. Traffic agent and ops agent they work in field and you will be in action always not like sitting in office and writing dozens of emails. As i said try to get job from handling companies most of them not looking for experience.
Good luck.