After you've made sure you're turning the correct way (as stated correctly above, if you are standing on the NONdriveside of the bike putting an allen into the spindle of a DRIVESIDE pedal, you need to turn clockwise. If you are standing on the DRIVE side of the bike, the same correct turn will be from that perspective counterclockwise. Either way, if the allen wrench is sticking UP you need to push it to the BACK of the bike.)

If it's still stuck, here's what I'd do. Put the bike upside down. move the driveside crank so it's sticking straight up. Since it's a hex wrench, you've got six choices how to put the wrench in, 60 degrees apart. Choose the position that has the wrench a little rearward of the crank. (If dead straight down is one of the six positions, that's a worst possible case, and the wrench-to-crank angle will be a relatively wide 60 degrees).

Grab the crank and allen wrench together in your hands and squeeze. Or try to immobilize the crank and bang the wrench with a hammer.

Alternatively, put the cranks horizontal, with the right crank to the rear of the bike. With two hands, lean all your bodyweight on the left/forward crank, and the end of the wrench. If necessary, extend the leverage of the allen wrench with a metal pipe (I have a removable handle for my car jack that works great for this)