Muscle Pain: Minor Tear or Just Strained?? (Chest & Arm)

I've been taking a break from upper body training for almost 5 days while attempting to wait-out pain I've been having in specific areas of my upper body. I'm beginning to become frustrated because the pain is not something I would consider severe and I expected a weekend of rest to be more than enough.
Essentially I believe I've developed some sort of strain or may have pulled muscles in my upper body from frequent push ups and other pressing exercises. I've never had anything like a muscle tear and I'm hoping there isn't anything like that developing.
The area of the pain is in the region of my upper chest (where the pectoralis minor overlaps the subscapularis) and upper arm (where the rear deltoid and upper portion of the tricep meet). This pain is a dull and most intense when doing exercises like push ups and bench press, or when my arm is half raised. This sensation is only on the left side/arm, and not present on the right side/arm.
I'm eager to resume training these muscles, but I want to avoid worsening what is happening. It seems like simple rest has not been enough for the pain to stop. I've been watching videos online that mostly suggest I should be doing some type of icing and massaging of the areas, but I don't really know what I am dealing with.
The pain isn't something that prevents me from doing light or even weighted exercises, however I'm totally okay with resting if it will facilitate faster recovery. Until anything changes I've simply put my upper body training on hold while focusing on lower body, stretching, and cardio to stay conditioned. That being said I'm getting a little stir crazy trying to wait this out.
What are some signs that I should see a doctor for something like this? Is this simply a result of over-training or muscle imbalances/weakness?
Hoping to get some feedback here from people who have dealt with similar pain or are experienced in dealing with pain in the upper chest/arm region. I want to get back at it!