An area of my gum is swollen. how can i tell if my tooth is infected?

See Dentist: Do you have other symptoms like tooth pain, have had a tooth injury, fever, or nausea/vomiting? Those may be signs of tooth infection, but if you think your tooth is infected, it is in general, best to see your dentist.

Might be infected: Gum swelling and pain can certainly be caused by a primary gum infection or an infected tooth. Strongly suggest an evaluation by your dentist.

Bleeding gums: You may have gingivitis or/and periodontal disease. Plaque is a sticky bio film that can be removed with a toothbrush, calculus is a harder and attaches itself to the tooth and root surface and needs to be removed professionally by a hygienist or dentist. See you dentist for an evaluation.

Check the tooth: Does it hurt when you touch it? How about when you bite on it? If it does not clear up in a few days you need to see a dentist.

It's Simple: See a dentist who is trained to evaluate these types of things.You are not trained and can't be expected to accurately determine whether or not your tooth is infected. That's true regardless of whatever we can describe to you on the internet. If you must know, swelling, pain, redness, heat and fever are typical signs of an infection.