EKG only shows the electrical rhythm of the heart, not necessarily a problem with the structure of the heart itself. An EKG can provide information about an MI, ischemia, abnormal rhythms, etc - an echo will show problems with the valves (in someone your age, possibly mitral valve prolapse), the heart wall itself, or congenital problems (sometimes people have a wall of the heart that does not close properly and must be surgically corrected). So yes, they are very independent and one can be normal with other being abnormal.
Chest xray was done to rule out infection (particularly pneumonia), but can also sometimes show other lung diseases (TB, sarcoidosis, etc). Chronic asthma can sometimes be picked up on x-ray, but only if it's pretty severe (the lungs look larger than they should and the diaphragm gets flattened out). Most other significant lung disorders that I can think of don't fit your age/history or are far too exotic to consider first before other things (there are some pretty nasty parasites can travel to the lung and cause all sorts of problems, including SOB as an early sign - really, though, these are somewhat rare so don't worry too much about this)
Anxiety must always be considered, especially if the discomfort in your chest moves from spot to spot throughout the week/month. If it is always in the same spot, it would make me think of other things first, but anxiety is ALWAYS a possibility that must be addressed.
I assume they've ruled out anemia?