Tessa,
Do you get back pain, knee pain, hip pain, ankle pain, plantar fasciatis, do you overpronate or have fallen arches?
If so, could be bio-mechanical, spent £25 and go and have a consultation with a proper physio/podiatrist.
Alternatively, shin splints can be due to too much too soon, i,e, the connective tissue takes longer to strengthen compared to muscle tissue, therefore you tear it and it hurts. in this case, rest till its better and take it a bit easier.Also, you can do lower limb excercises.
good luck