hello and welcome,
normally,deep cleaning will not cause any kind of pain or swelling over gums and cheek other than sensitivity unless any trauma occured during the procedure while using ultrasound
scaler and hand instruments.
have you got checked for any decay or impacted wisdom tooth
in your right side?
without clinical examination,we cannot decide your diagnosis and treatment plan.
if you have severe gum infection
, i advice you to take tab.doxycycline.100mg once a day for 3-7 days depending on severity of the problem.please give your medical history like epilepsy,cardiac disease etc. to your dentist
so that doctor can give a proper diagnosis.
hope you get well soon.