Dear B.,
I had the same problem when I was your daughter's age, though mine would occur soon after going to bed. I'd run around all day long (I lived on a farm), then the growth plates in my legs would swell a little when I stopped walking around on them. Oh, the pain! I'd writhe in bed, begging for a baby aspirin (this is 43 years ago). If you've ever had a heel spur, the pain is very similar, and a heel spur hurts the most when you take pressure of it and it has a chance to swell.
See if she'll take Tylenol or children's ibubrofen before she goes to bed and see if that helps. The ACE bandage sounds like a good idea, too. Four is not too early for "growing pains" as I can attest to. You should take her to her doctor just to make sure nothing else is going on, but don't be surprised the doctor says it is growing pains.
My four year old daughter hasn't complained of her legs hurting, yet. I'll understand her when she does, though, and be ready with whatever she needs rather than dismissing her as a "faker".
At the moment, I can tell she is growing again because she has become more accident prone--two nasty skinned knees last week.
Hope this helps.