Hi Gingerbaby-- welcome. I didn't read all the answers here but I'm sorry your pediatrician is so dismissive. I have twins and another child, and based on my experience, I think the sleep issue is an inborn trait, not necessarily anything you're doing.
My PG twin slept through the night at three months. He was then and remains now a huge sleeper. He can still sleep 15 hours at a stretch if he has time. (He's 13.) As an infant and toddler he would take five-hour afternoon naps, and still go to bed for the night at seven. We always had to wake him up from naps because otherwise he would just keep sleeping.
His HG twin, on the other hand, hardly ever slept. He didn't sleep through the night until he was two. (Sorry to tell you.) We briefly tried cry-it-out when he was about 18 months old, but I couldn't take his crying out, "Mama! Mama!" Poor guy. He dropped his morning nap by 6 months old and only napped for an hour in the afternoon. He still is early-to-rise, up by 6 every day of the week, and puts himself to bed by 9:30 most nights. He knows what he needs and sticks to it.
I know it's challenging when you're sleep deprived, but I would try not to worry about it. Your child will be sleeping more soon-- in the next year, certainly. I would also try to make sure your child isn't overtired at bedtime because that always led to poor sleep for us. There was a prime sleep window-- one before the meltdown. I would also make sure he has plenty of activity during the day.
