Is gum swelling linked to other diseases of the body?

Yes...can be. There are numerous diseases that can affect the gums. I would suggest a consultation with a periodontist and see if you have gum disease and whether a consult with your physician is indicated.
Yes. For example it's the 6th most common finding in patients with Diabetes. Associated with, increased risk of heart attack, increased risk of stroke, associated with liver and kidney disease. Swollen gums usually mean infected gums. Would you let any other infection go untreated, I think not. Please see a Periodontist, a gum specialist, to Tx dessert before it becomes intractable. Also see MD/DO.
Bad gums; illeness. Swollen bleeding gums may just be that. They can also be related to other systemic disease like diabetes, lupus, and other immune suppressive diseases. If a dental cleaning does not clear this up, or you have not a physical exam within a year seek a medical consult to evaluate your overall health. Its important.
Maybe. Swollen bleeding gums can be a sign of a dental problem like periodontist which itself has many causes and needs evaluation by a dentist.