Could you provide a link of the one you bought? I can't recommend a specific one. The only I have is extremely old and simple build (like so old I don't even know the brand or anything) made out of metal and is going through pretty much anything lol.
It could be that you either didn't use enough pressure, because you do need to pressure quite a bit, depending on the laminator paper and drawing paper OR the hole puncher is simply not suitable for it.