Can tense muscles in my back cause a preasurre like sensation in my left side chest with spasm like feelings every once in a while?

Pressure: Yes. A back spasm could possibly cause chest wall pain in the front. This can occur especially if the spams is significant enough to compress a disc or impair posture.

Muscle pain: With your age being young and low risk for life threatening disease such as heart attack or aortic dissection, muscle pain like costochondritis from strenous activities or even position on sleep or use of accessory muscles of breathing like coughing wil most likely be the reason. However if the pain is very severe and causes lightheadedness and shortness of breath, you need to be examined.