What is the cause of cracks in the corner of my mouth and sore swollen gums with red spots inside my mouth?

Angular Cheilitis: You may be suffering from angular cheilitis, which can be fungal or idiopathic in nature, or even a result of a nutrient deficiency. Not sure if the gingival issues are related, but a visit to your dentist and/or physician should provide you with additional guidance and treatment.

Multiple symptoms: Cracks in corners of mouth may be angular chelitis which seems to respond to B-complex therapy. Swollen gums w red spots may be a separate and distinct problem. Please see your Dentist for evaluation and treatment.