It can take a while after illness for toddlers to become comfortable to sleep independently again. The illness may have brought on some SA, but even if it has not and he is 100% over the illness, he is approaching his birthday which is a prime time for a good bought of sleep disturbance and separation anxiety. So there are two quite common causes for SA which may be having a real impact on how your child is feeling at BT.
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He ended up putting our son down on carpet to sleep and he walked out.
Why was he on the carpet instead of the crib? Have I misunderstood something? Was your DS still crying?
Please know that at BW forums we believe in responding to your child's cries to maintain the bond of trust. Whether a child is suffering a phase of SA or not we do not agree with leaving a child to cry alone.
I suggest you sit by the crib when your son goes to bed, place a hand on him if this is helpful, and continue to reassure with your voice. A key phrase can be very useful to repeat such as "I'm right here, everything is fine, go to sleep" or simply "it's sleepy time". There is a world of difference between a child crying with a parent present and a child crying alone.
It may also be helpful to look at your routine. If he is UT for BT this can cause a lot of fussing and call backs, needing extra help to sleep despite his ability to sleep independently for naps and for BT prior to his illness. If he is stalling BT by 15-30 mins I would probably start the BT routine 15 mins later and see if BT is calmer or look at the whole day routine and see if anything needs a change.