I have a small mouth ulcer and sore throat. the ulcer is directly below a molar with a severe cavity where the cheek meets the gums. is it connected?

Mouth ulcer: That ulcer may be in fact an abscess due to the cavity of your molar. See your dentist ASAP

Aphthous ulcer: Its not uncommon for the stress of an oral infection to trigger aphthous ulcers. However, given you also have a potential adjacent apical root infection, it may be due to an underlying abscess and require urgent dental evaluation. In the mean time, keep your mouth clean with luke-warm salt-water swish and spit and avoid traumatizing the ulcer with aggressive dental brushing. See your dentist.