4 Year old girl... does she have SPD?

I am a teacher of a Pre-K classroom which I have been with for 3 months. I have a 4 year old girl who I just don't know what to do with anymore. She has always had a problem paying attention and is often in her own world i.e. dancing around, saying nonsensical things, zoning out. She was doing okay for awhile, but over the past month she has started being very disruptive at nap time. She laughs to herself and in the teachers faces saying nonsensical things. It's like she can't control it.

My other teachers and I have tried being firm with her, tried being very sweet, tried ignoring her, etc. We gave her toys to play with at nap, which lasts her a few minutes, then she is off again. I feel like things are getting worse and we are not helping ourselves or her. Do you think she may have a sensory processing disorder? If so, how can we help her/ourselves?

By the way, she often likes to go to the art area, pour out glue, and put her fingers in it. Also, instead of painting with paint we offer on certain projects, she rubs them on her hands and arms, washes it off, then rubs them on them again.