Brief Answer:
It could be mild shin splints which will fade away by rest , icing , compression bandaging , elevation of feet and some gentle massaging by topical gels .

Detailed Answer:
Hi i am Dr Ahmed Aly
thanks for using HealthcareMagic site ,
I had gone through your question and understand your concerns ..

I think you may have a kind of shin splints , do not worry it is very common to have such feeling if you over stressed your legs while long walks or running .
You mentioned in your given history that you favor that leg or depend more on that leg . shin splints is more common in the dominant leg , people with flat feet , athletics , soccer players etc .
For now you may avoid over weighing , heavy lifting , vigorous movements , any kind of sports till your shin muscles rest . apply RICE ( rest or relax your muscle , icing after exercises to prevent inflammation and reduce pain , compression bandaging will be helpful , elevation of your leg will decrease swelling progression ) , on the counter painkillers like NSAIDs tylenol tabs when needed will reduce inflammation and pain , with minor stretching exercises will be more than enough in your case .
medication in mild cases is not needed only rest and relax will be fine , in moderate to severe cases NSAIDs ( non steroidal anti-inflammatory drugs ) tabs will be helpful , gentle massages with topical anti-inflammatory gels , muscle relaxants , B12 vitamin supplements will be effective in most of cases .
If pain persists with edema or excessive swelling i recommend X rays and some lab investigations and follow them up with your orthopedic for proper evaluation and managment .
Please click and consider a 5 star rating with some positive feedback if the information was helpful. Wish you good health,
Any further clarifications feel free to ask.

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