My stomach problem is that I feel full after eating not that much. Is that a sign of heartburn, but without the pain?

Early satiety. C MD. Getting full after not eating much (especially if that is a change) is a symptom that needs further evaluation. Lots of things, some very serious can cause that, including ulcer, mass of esophagus, stomach, duodenum, liver, big spleen, lymph nodes. See your doc asap.