As someone who has repeatedly had shin slints on and off for years, I wouldn't worry so much.
It sounds like the change of surface has caused you to subtly change your gait (such as a change in the degree of pronation (or inward foot-roll.)) The exact same thing has happened to me - I always ran on pavements / roads but one run on a gravel path and I'll be aching all over and specifically, have the same ache in the outside of my lower leg.
Shin splints (AKA medial tibial stress syndrome) is an inflamation of the tendons where the big muscle in the front of your leg (lift your toes towards your knee to feel which one I mean) joins to the bone. Some people incorrectly use 'shin splints' as an all-encompasing term for lower-leg pains.
If you only ran on this new surface once and felt discomfort, it's likely not shin splints, which in my experience takes time to develop. Likewise, if the feeling is more of a tightness than a specific area of pain, I would'nt worry yet. A new surface will take time to adjust to - just phase it in a little at a time.
Shin splints is more likely to occur on the inside of the shin bone, just above the ankle.
Some criteria for identifying shin splints are:
- If the area is tender when you press on it.
- If the pain occurs at the start of a run while your muscles are cold, but reduces as you warm up
- If it's a 'bone pain' rather than a 'muscle pain'
As for a cure - this is much more difficult because its hard to identify what the exact cause is. Some people will recommend stretches or exercises for your lower leg muscles but the cause could also be weak hips (it was for me), or simply poor running form. You are far better off seeing a physio if you're sure its shin splints than wasting time self-diagnosing. They'll get you on a treadmill and look at how you run to see what the cause is.
To treat the symptoms an ice pack for 20 minutes will work wonders.