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You can drench your hair in water and pin down tightly overnight. The cowlick will definitely be not strong.
Or try to gel the hair down flat at the cowlick area overnight. Wake up and brush gel
Blast hair dry right where cowlick is close up and flatten cowlick while blow
By ruby mae 
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Here are questions related to Getting Rid of a Cowlick.
I have this really annoying cowlick. My hair is kind of straight. I just got a side fringe and the side fringe kind of curls around. I don't want to be straightening my hair the whole time, so please give me some advice.
By Jane. W from Ireland
I think you try to modify you current method (headband). First dampen it, just use wet comb or fingers and brush through that area (aim wetting the hair roots) and then spread the water evenly within that area. You shouldn't wet it so much that the water drips.
Does anyone have a remedy for cow licks? I have tried blow drying in the direction, gel, etc., but with no luck. Have you used a particular product and/or a technique that works? Thank you!
My best and I both have cows licks at the front. She has being taming hers 3 months and now so has a sweeping fringe. I have been tryin it the same way and it does work. She taught me to try using other parts of your hair and covering it to weigh it down. Pull hair form the back of you head and move it forward over the cows lick. It is workin also straighteners do help. It has worked so well for her and her hair is lovely so I just hope mine goesthe same.