Most nosebleeds are usually not serious and can be stopped with home treatment; they occur in the front of the nose (anterior epistaxis) and in only 1 nostril. Some blood may drain down the back of the nose into the throat. Common causes:
Changes in the environment: Cold, dry climates; low humidity (applies to your case). High altitude. Chemical fumes. Smoke (also applicable to you). Injury to the nose. Blowing or picking the nose (the jumping might have had the same effect). Piercing the nose.
An abnormal growth inside the nose like nasal polyps, or a deviated nasal septum (a deviated nasal septum is very common &makes you more prone to nosebleeds).
Colds, allergies, or sinus infections. High blood pressure. Kidney disease. Liver disease. Blood clotting disorders (these usually run in families, like hemophilia).
Those that affect blood clotting, such as aspirin, warfarin (such as Coumadin), enoxaparin (Lovenox), clopidogrel (Plavix), or nonsteroidal anti-inflammatory drugs (NSAIDs).
Cold and allergy medicines
Steroid nasal sprays
Nasal abuse of illegal drugs, such as cocaine and amphetamines
A less common but more serious type of nosebleed starts in the back of the nose (posterior epistaxis) and often involves both nostrils. Large amounts of blood may run down the back of the throat. Posterior epistaxis occurs more often in older adults because of other health conditions.
In your case, it could be a combination of environmental exposure to the AC (cold air), cigarette smoke, vigorous jumping,aallergic baseline (if you regularly sneeze and have an itchy nose), &a deviated nasal septum (if severe). You need to keep your nostrils well moisturized (apply a thin layer of Vaseline petroleum jelly daily using a cotton tip) plus nasal saline (like Nasocleanse). If you're concerned about underlying disease, check with your doctor.