Even if you go to a specialist without a referral, which many health plans allow (ours do), I would still suggest changing pediatrician.
There are good ones out there - we love ours a lot, who always take the time to discuss issues and his reasoning and he has never dismissed our concerns (in fact, he flagged a few things that were critical when we had not realized it was serious). He was the one who caught a co-worker's daughter's diabetic condition early enough that the children's hospital were impressed he detected it. So there really are good pediatricians out there.
I know my parents regret listening to their doctor when even a family friend who was also a doctor told them that I should be checked out - their concerns were also brushed away as "she is fine, she will outgrow that" and by the time I was checked out, I was almost 4. It took years of remediation and work to make up for the gaps I had developed in those early years.
