Does severe shoulder pain also cause chest pain?

Left shoulder pain has been gradually increasing, and lately I’ve even started to feel a slight pain in my left chest. I’ve rarely experienced shoulder pain in my life, so I’m a bit worried. Usually, applying a patch would quickly relieve the pain, but this time it’s lingering strangely longer. Also, not only my shoulder but the same side of my chest is aching, which worries me a bit. Applying heat packs and doing stretches seem to help somewhat...

I will go to the hospital, but should I first visit the orthopedics department?

Has anyone experienced chest pain along with shoulder pain? When I searched, it said that heart-related conditions cannot be ruled out, so I'm a bit worried and scared.