-->Go to primary care Dr......and possibly get a generic neoprene knee sleeve. He'll likely send you to PT.
-->Go to PT....hopefully one that is good. If it's purely a MCL sprain, the PT will be able to help you through the whole thing.
The MCL is essential to the stability of the knee which is why you feel it quite a bit with general walking, weight bearing, etc. Also, because you can aggravate it with general walking, it can take a long time to recover. Also the MCL (being a ligament) is not greatly supplied with blood.....so, healing is slow.
If the PT is worth their salt, they will be able to tell you in a few wks if things are going to go well. If things aren't going well, you need to get in to see an Orthopedic Specialist. A portion of the MCL attaches to the medial meniscus.......which "could" indicate a tear. Now, it's not all doom and gloom. Sometimes just more time is needed in PT. But on the rare occasion you do need surgery. And, yes, surgery for a MCL/MMT is far less common than other knee surgeries. In the vast majority of the instances, PT will get you there.
--Signed a ATC turned PT for a prominent Orthopedic group.
And, no, an MRI is not needed and is a waste of time and money right now. An x-ray, on the other hand, is worth the time/money right now.....but is not 100% needed.