Thats good to hear. It sounds like it's improving well.
Your frinds thoughts are good. (P)RICE(D) management is first aid for any strain or sprain. If your unfamiliar: R= rest I= Ice C= comprssiong E= elevation. P means either prevent or protect depending who you talk to and D means diagnosis. Forget all that however because as I said that is first aid - remember it for the future, as you don't have swelling and your now past the inflammatory phase RICE'ing is no longer really that important for you.

All going well - If you continue to improve as you are now, you can be relatively confident that you did a contusion, They can resolve without physio relatively quickly depending on the severity.

I suggest as always to seek help, but given you are now only getting pain by pushing on the area then I'd look at doing some quadricep stretches if you aren't already. Massaging will be fine as your past the bleeding phase now. If you can do a quadricep stretch pain free and can do a deep squat without much trouble then your very likely ready to start light jogging and building it up as you see fit to something a bit harder.

Let me know how you go.
And always RICE in the future if you don't already.