Hi. I built the laundry basket dresser for a friend out of MDF, my first time using MDF. Used 2x2s for the supports but when we try to screw it in (from the inside, going through the wood first) once the screw tries to go into the MDF, it kind of pulls away and leaves a slight gap and the glue just comes dripping out. Used a clamp, however, could only use one from the front since the back was already on. Would it have been better to screw from the outside going through the MDF first? Frustrated. It might seem ok now, but I don't want to find out over time with weight from clothes the supports give way!
You'd just experienced something called bridging. The preferred solution to that problem is a screw with an unthreaded portion of the shank. Screws are available with different lengths of unthreaded shank, but I'm not sure how to go about finding them.
The alternative is to do just what you did: clamp it so that gap can't develop in the first place.