I would say adopt a wait and see approach - she may well change significantly in the next 6 months, especially with the speech therapy. But I would also say try, if possible, to get her into some type of preschool-type program, even if it's only a couple hours/three times a week. It will probably be hellish in the beginning and even for several weeks thereafter when you drop her off, but it will make life so much easier when/if you put her into a pre-K program next year.
My son, who has always been kind of shy, went through a really rough patch last year shortly before his 4th birthday. He would not go into any type of activity class alone, would not sit in a circle with other kids, did not like to be looked at, especially by other adults, had huge meltdowns at swim class, refused to go into a bounce house with other kids, refused to wear his Halloween costume, refused to go to a Halloween party, and hid his face in his hands during his entire Christmas school recital when all the other kids were singing. He had at least one massive meltdown a week, which was unusual for him. To make matters worse, he was apparently having big, frequent tantrums during his new nursery program, enough so that his teacher thought he had an underlying condition. I won't go into THAT whole story, but obviously I was very worried.
I was advised by a handful of wise people to wait it out for four months and see if he progressed/changed. Four months later he was a different person - he didn't cry or cling when I left him at school and the in-class tantrums evaporated. He was more willing to attend activities, sit in a circle and even - gasp! - answer questions from the instructors. He even SANG at the spring recital. Didn't cover his face once. I was floored.
He still can be anxious and shy at times, still likes to hide behind me when walking into new situations (or even familiar ones), still screams in swim class :(, but he is so much more confident and independent now. A new kid.
So, try to get her into a program if you can, weather the first few weeks of torment and check her progress in a few months. If you see NO changes, then I would pursue the topic with your pediatrician.
Best of luck - I think it will all turn out fine!