Hello,
Has it been a long time since you have had a dental exam and cleaning? You may have an infection, bit your cheek or something caught under your gum. You can rinse with warm salt water, but schedule a dental visit. There may be more problems than just inflamed gums. The teeth stabbing your gums may be a wisdom tooth errupting. If you do not have enough room for the tooth to errupt, an extraction should be considered. A cleaning can reduce inflammation of the gums and is clearly recommended. Your statemnet of a jagged tooth makes me concerned that a tooth is broken and needs evaluation by a dentist. Over the counter pain and anti-inflammatory medication should offer some relief until you schedule your dental exam.