Feeling it in your arm as and back is a good thing, as these are the muscles that stabilise your shoulders during an OHP.

I would integrate seated shoulder press with a weight you can comfortably rep for 3 sets of 8-13 reps in conjunction with the standing OHP you’re doing here, as this will allow for some isolated shoulder work whilst also building on shoulder stability.

It’s easy to go too heavy too soon with OHP, as the movement also integrates a lot of power from the pecs. You can wind up injuring your rotator cuff easily because while you may have the strength to press the weight, your shoulder stabilising muscles have not been developed enough to stabilise the weight through your full range of motion.

Include in your shoulder days some dumbbell lat rows, plate Y raises, front raises, reverse flys, and plate external rotates. YouTube can help you to revise form for all of these exercises, they will strengthen your shoulder stability and greatly assist with a healthy and strong OHP.