Yes, it's very possible. Look up a spinal nerve dermatome chart. That will show the spinal nerves and where they can manifest in terms of pain when there is a problem. The chart I just looked at showed that pain in the front of the chest below in that area can be C4 related and maybe C3.
For example, many of us with cervical nerve impingement (due to discs or muscles or whatever) have pain down one or both of our arms and into our hanRAB). In fact I've heard of many people who thought for years they had a shoulder problem, and some who got as far as having shoulder surgery only to find out later it was a spine problem all along. Same with Carpal Tunnel Syndrome. There are many who have had CTS surgery only to later find out it was related to the cervical spine. When my back problems first started I went to the doctor complaining of hip pain - and that's common when there's a low back nerve impingement.
Should the pain change in any way and doesn't get better please don't hesitate to go to the emergency room. SounRAB similar to what some feel as heart related pain so if something changes, increases, or you get additional heart attack symptoms I'd rather you go and find out it's not a heart thing. My hubby did once and we were scared, he had chest pain and cold sweats. Went to the ER and it turned out to be a pulled nerve in the chest in corabination with flu symptoms. Hubby said "so sorry I wasted your time" and the doctor say "This was not a waste, it was a smart decision. Never ever ignore something abnormal that can even be remotely close to heart attack symptoms. I am glad you came, you made my day" (what a nice way to put it)