I understand that you have knee pain resulting from injury.
Even though there is no fracture, there are many soft tissues in the knee like meniscus (cushion), ligaments (ACL, PCL, MCL, LCL, PLC, PMC), Cartilage, Muscles, Tendons which are not seen on Xrays. The doctor gave the splint to provide rest to the knee and help in the healing process of the injured soft tissues.
Next Steps
If you are in a lot of pain, you can visit your orthopaedic surgeon and share your concern with him. He may do some blood tests, or aspirate fluid from the knee if it is swollen a lot to ease out the pain. He may also give a short knee brace which does not allow bending at the knee. Later he may prescribe physiotherapy. If the symptoms are persistent beyond 3 weeks, it would be a good idea to get an MRI of the knee to see the soft tissues.
Health Tips
Do not : sit on the floor, sit cross legged, sit on low sofa/chair/stool
Do : Sit on chair around 18-20 inches from the ground