Hi T.,
Is your little one's crib new? If it is, the mattress is probably still outgassing the synthetic chemicals it is made of (unless of course you bought an organic cotton one that most of use can't afford :). These chemicals are terribly dangerous and are linked to SIDS as is chlorine bleach that is used to disinfect bedding. If it is new, let the mattress sit outside for a couple of weeks on a covered porch or carport. If it's made in China, you may need to let it sit out a little longer. Also Urine mixed with some of these chemicals make it worse so make sure baby doesnt leak a lot. Nightmares and night terrors can be provoked by neurological stimuli like the toxicities in laundry supplies and new bedding and the multiple combinations of chemicals.
The reason that many think that tummy sleeping is dangerous is because the baby's face is directly in the mattress and laundry detergent. These two things can also contraindicate like other chemicals, e.g. pharmaceuticals, and mix a deadly cocktail. Not all little ones know to move their faces if they are in respiratory distress.
If you use non toxic laundry products (non toxic for humans not just the environment) and your mattress has outgassed most of the chemicals already, your little one should stop having nightmares/terrors. Detoxing your home can be simple and very inexpensive. Most people think it is costly and it can be if you don't know exactly how to shop. My house has been detoxed for 7 years now and my household budget/spending is less than it was before we detoxed.
Hope this helps!
M.