My son had a pimple on friday. it has developed into a deep brown purple scab and his entire arm is swollen. no pain though?

Possible bug bite: A pimple like lesion followed by swelling and redness WITHOUT pain is likely to be related to a bug bite of some sort. Cold compresses and elevation usually helps. If there is possible exposure to ticks or if this is painful, evaluation by a doctor is important to consider infection or cellulitis. Antibiotics might be indicated.