Mid way is mostly muscle - Biceps brachii, brachalis with triceps in the back of the arm. They’ll hurt today but there’s no overly exposed nerve areas like the side of the neck or in the armpit (axilla). You may want to consider ibuprofen or a compression sleeve if you have one on hand. Worst case make a sling so the muscle doesn’t have to support the weight of the arm. It sounds like you’ll develop an intermuscular haematoma aka corky aka charlie horse, they suck but there’s not a lot that can be done about them.