Hello Jordie,
There are, as with all things, several available approaches. In the western medical model there are certainly benefits, however their view treats only the knee rather than the entire body (allopathic versus holistic) and typically uses pharmaceuticals and surgical remedy as tools.
What sits well with me in advising students is to suggest they consult with the healthcare practitioner of their choosing. Be that an orthopedic, osteopathic, naturopathic or shamanic practitioner is not for me to say.
Some injuries to the knee will subside, these include sprains and strains. Others will not simply disappear but will need to be addressed. These include damage to ligament and tendon. And, of course you’ve not supplied enough information to really give profound guidance, for example you do not mention if the joint is swollen.
Since you ask about “healing exercises” I’d like to mention two things. First, it is irresponsible (for me) to offer such things without contact hours and assessment.
Second, “yoga”, simply in title, is ill-advised. HOWEVER, a yoga therapist who understands and is trained over time in applying all of the tools of yoga (including breath work, light work, meditation, lifestyle/nutrition, and appropriate asana) could be very supportive of your innate healing powers. Such teachers are incredibly hard to come by as most teach only poses. And again poses for you at the moment are ill-advised.
There are therapeutics for the knees though and this should not be discounted, overlooked, or dismissed simply due to a lack of having experienced it.