You might be ironing the parts in the wrong order, or getting the freshly ironed part under something. But the first thing I would try in your position is to just iron every part of the shirt and hang it up for a while, and then see if the wrinkles go away again. Often wrinkles that come about right after ironing are much softer than the ones that you remove by ironing.
One right order is: Collar, yoke, one arm [cuff first], other arm [cuff first], front left, back, front right.
Are the wrinkles pretty much the same ones you started with, or are they new ones with sharper creases?
If new, sharp creases, you are probably accidentally ironing creases in the wrong place, or folding it over as you go. Concentrate carefully on the placement of the garment, remembering that fabric will remain prone to creasing while it remains hot.
If original wrinkles which have not gone away: You are probably not using enough heat and steam. 100...
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.