Having 1 son with seasonal allergies diagnosed at 1 year AT MY INSISTANCE, and the other one passed the typical skin test at one year but is being treated for allergy induced asthma, allergies are there prior to 3-4 years.
I'm curious about the apnea. My 9 year old was diagnosed at 4yrs., and reviewed this past Spring. It's gone but Periodic Limb Movement was diagnosed from the second study. I have narcolepsy. If I eat too many carbs (sugar), it will force me to nap. Everyone is different, my limit is 5 grams at a meal and no more than 10 grams in a day of sugars from breads products, 1 raw fruit, and no more than 7oz. of real juice a day. I also can not handle turkey, apples or peanut butter. My dad (has apnea) however can handle cooked apples.
You're MOM, you feel this isn't just a typical baby habits. Ask more questions. The doctors often try quick fixes or what works for most everyone else. Thankfully, my insurance changed a few times and I chose to switch doctors a few more times. We have a wonderful team now that listens and knows when I'm making a mountain out of a molehill, and when we need to look into something further.
We also learned to avoid all dairy products. It's a stimulant to my boys and me. We sleep, but not well, and it makes my youngest and myself very moody.
Just my experiences...
I don't have a clue how the fact that he's a preemie figures into all of this. I just know that it does.
Good Luck