What causes Paresthesia (Pins and Needles) at a cellular level?
Underneath the superficial layers of your skin there are receptors which sense pressure, temperature and pain. These receptors are part of the peripheral nervous system which senses stimuli and they take the message conveying details about the stimulus to the somatosensory cortex of the brain. Here is where the perception of pain, burning, pressure etc is ultimately made. To take the simplest example, if you stop blood flow for a short amount of time in a limb, these receptors are activated, and will send signals to the brain that are interpreted as tingling or numbness. With more severe pain, different receptors are activated which , again, project to the same brain area but a different message is read out. If the pressure from one limb is removed, the receptors will go back to normal function as blood flow is restored.

https://en.wikipedia.org/wiki/Nociceptor

http://www.scholarpedia.org/article/Mammalian_mechanoreception