It's hard to diagnose these things via a forum but here are my thoughts;
Ligament injury is unlike due to lack of trauma, swelling or giving way.
Patellofemoral pain is unlikely as you can squat pain free and the symptoms are more medial.
Referral from another joint (e.g. Back or hip) is a possibility but wouldn't usually create such a specific area of pain around the medial knee (I'd expect symptom in the thigh, hip, groin or back as well)
An issue with the medial meniscus is a possibility but I'd expect pain squatting and joint line tenderness. I wouldn't rule this out though as it could be more a problem with the anterior part of the meniscus causing pain when walking.
The other possibility, which may be more likely, is the fat pad beneath the patella tendon. It can produce pain in several areas around the knee. Really though you'll need an examination to make a clear diagnosis.
I'd ice the painful area 15 mins, twice per day. Run only if pain free. You might be able to do short distances but it needs to be comfortable during the run and for 24 hours after. Taping can really help to offload the fat pad. This one from RW is very simple but can be very effective;
http://www.runnersworld.com/article/0,7120,s6-241-286--13018-0,00.html
Try it then go for a walk, see if it reduces your symptoms.
Also try stretching the quads as if they are tight that can increase the stress on the fat pad. Have a good stretch session then again see if it helps you symptoms when you walk - in that way you can test if it's helping.
If it's not settling and still painful walking after giving this stuff a go then I would get it assessed properly.
Hope that helps
Tom G