Most of the responses here have already hit on the important parts so I'll just add a little extra.

When you sense touch, that signal is sent back to the spinal cord and then up to the brain. That signal is interpreted by your sensory cortex which has a map of your entire body called the homunculus. So when your shoulder is touched, the some of the neurons in the shoulder part of the sensory homunculus get activated which your brain can then interpret as a touch on the shoulder. Scientists have seen that the distribution of neurons is not equal to the surface area of your body parts. Just because you have more shoulders than hands doesn't mean you have more neurons dedicated to sensation for your shoulders than hands. In fact, its quite the opposite. Your hands, particularly the fingers, have a high density of sensory neuron endings making them exquisitely sensitive to touch. Your shoulder (and most other skin) has much fewer nerve endings and is less sensitive and thus takes up less of the sensory homunculus. This is why you can feel fine details with your finger tips but not with your shoulders or even the back of your hand.

Pain is interesting since there are pain sensing neurons in for both your somatic nervous system (skin, muscle, things under conscious control) and autonomic nervous system (stomach, heart, things under unconscious control). We are not very good at localizing pain coming from our autonomic nervous system which is why, for example, stomach aches often feel like a more generalized pain/unease. This phenomenon is also why appendicitis will first present like a stomach ache or cramp (autonomic pain) before eventually becoming sharp/burning pain in the lower right quadrant as the inflamed organ begins to irritate the skin above it (somatic pain).

Sensory homunculus - https://www.ncbi.nlm.nih.gov/books/NBK549841/

Somatic vs autonomic pain - https://journals.physiology.org/doi/full/10.1152/ajpgi.2000.279.1.G1