Is the crate big enough? You need to have a bed at the back and newspaper or puppy pads at the front, so the pup can come to the front and poo on the paper. A 3 month old puppy is still very much a baby and cannot be expected to hold it all night if it needs to go.
Gradually you will find that there are some nights when there is no poo, try setting your alarm an hour earlier and try to catch it before it has gone. It could be that the pup is only going just before you get up.
I hate to think what you are spraying, but please don't, as you will end up with a neurotic dog that is scared in case it poos.