Injured my thumb not broke tender too touch around the CMC joint area and stiff/swollen should I keep in splint?

Splint. If there's still tenderness and swelling I recommend keeping the splint on. Even without being fractured, there still can be significant damage to the joint, and I recommend an evaluation by a hand surgeon for proper diagnosis and treatment. You want to prevent permanent damage to the thumb if this injury is not properly diagnosed and treated.