Hallo
MCL = ligaments which run down the inside of your knee. They either get damaged by trauma (ie foot kicked away from you, whilst your knee rolls in) or repetition (ie dodgy mechanics like a flatish foot, poor glut control which lets your thigh roll in).
Training your quads is generally a straight line affair and doesn't control the knee being forced in. Don't get me wrong you need good quads strength and control BUT don't forget about controlling your thigh rotation (gluts) and foot pronation (rolling in = proper shoes).
As long as the damage is mildish, give yourself 4-6 weeks to get stronger, get stable and get savvy!!
Cheers
TPV