Your symptoms are concerning. I would recommend that you see your primary care doctor
to have this evaluated. If required, he or she may refer you to a orthopedic surgeon
who specializes in problems of the bones and muscles.
To answer your question-- YES. It is possible to cut (or more accurately tear) a muscle without a significant tear of the skin. In fact, a muscle sprain is actually a small degree of tearing of the muscle. If this is severe, there can be partial or even complete tearing of the muscle. The quadriceps muscle in the thigh is actually a large muscle with four distinct parts, as such is is possible to hurt some or part of it and still retain strength. The misshapen nature of it is also concerning.
There are other considerations. Infections can form under the skin and persist. In addition, scar tissue or calcification can form in the muscle and cause problems. Beyond the muscle, there could have also been damage to the nerves which could be causing the pain.
Another consideration is that you should ensure that your tetanus shots are up to date. This is important with any scratch or cut from a dirty surface.
Talk to your doctor.