Try looking up the dsm-iv for depression. That lists criteria needed to be diagnosed.
Very basically: low energy, low mood, either too much or too little sleep, changes in appetite (either increased or decreased), trouble concentrating, etc. Maybe thoughts of suicide.
Are they linked? If anything, untreated reflux is enough to make anyone depressed (through pain, sleep deprivation, etc).
Depression may lower immunity making one more susceptible to illness.