Getting Shin Splints really has nothing to do with bone density. Hopefully that's all you have and not stress fractures. Stress fractures are general impact related. If jumping impact hurts that may be the case. Having stiff calf muscles, ach tendons, arches etc can also effect the shin area. I am not a doctor, consult a doctor. What I know, is from personal experience. Both injuries are common "overuse" conditions. There really is only one solution - rest. That means absolutely nothing for 6-8 weeks that causes any pain at all - that's from my PT brother. What's odd - I developed a stress fracture from running/sprinting, and biking was one of the suggested methods of recovery. Same issue, jumping on the leg hurt. Very localized acute pain. Slight bruising. Getting an x-ray won't even show anything until you're mostly healed, and the injury calcifies. Stay off the leg, don't do things that hurt. Call your doctor and or Physical Therapist and have them take a look sooner than later. In the end, all you can really do is rest. Ice and advil help
ed me at first when the pain was greatest. Talk to a doctor.

Note: I have been a powerlifter for 15 years. My bone density is way above normal, or so ive been told-and partially because of genetics. I've never broken a bone (two minor fractures). Because of my weight, I have to be careful of impact exercises, and related overuse, though in my case it was barefoot running, and progressing too fast that got me. My own fault. I stopped running completly for 4 months, and started back slow. Ironiclaly it was recovery trainig on an exercise bike that got me into road cycling. 4th time - see a doctor, at least talk to one, and don't do things that cause pain or it's not going to heal. It's not rocket science, nor is there a magical fast solution.

Summary: Consult doctor, avoid pain, rest, I am not a doctor