Have seen a cardiologist and he said nothing wrong. Could anxiety cause my heart rate to go up to 144 climbing stairs and then heartburn?

Anxiety shows itself. In may ways. Once can mentally obsess over things that frighten the person or do behaviors to keep danger away, e.g., ritual behaviors, checking and re-checking. Physically there can be heart palpitations, shortness of breath, sweating, sleeplessness, etc. Please go to a mental health professional for support . See www.relaxationresponse.org for a self-help tool.
Possible. Do you have anxiety? If yes, then possible, but a TSH (Thyroid Stimulating Hormone) should be obtained. The rate of 144 is twice normal so both might exist.
Elevated heart rate. Sometimes anxiety can cause elevated heart rates. Sometimes elevated heart rates can cause anxiety. Not sure what workup was performed. Consider a cardiac monitor to assess overall heart rate. Possibly may be experiencing inappropriate sinus tachycardia. Usually does not cause heartburn but some people do complain of chest heaviness or symptoms similar to heartburn.