Wrist pain when holding mug and loss of grip strength like holding pen. New onset. What is happening?

Many possibilities. Most common is carpal tunnel syndrome, where median nerve is pinched in wrist. Also can be nerve injury or disease, muscle disease, stroke. Your doctor should be able to start workup. If you have stroke symptoms (speech issue, other weakness), call 911.
Arthritis possibly. Carpal tunnel syndrome and basilar thumb joint arthritis are the two that have these complaints most frequently. The only way to know is get it evaluated by your hand specialist. Ulnar nerve problems can also manifest this way.
C A hand surgeon. You should see a hand surgeon for an evaluation and x-rays. This could be due to an old injury, joint, nerve and/or muscle disorders.