My best advice would be to do what you were advised to do and SEE a physio. To give you a true prognosis, your ankle needs to be assessed. A physiotherapist will be able to assess the ligaments of your ankle and tell you what damage has been done, generally how severe it is and what you can expect from the future. If there is no full tear (which is very possible considering you never noticed any swelling until the next morning), there is no reason that you can't get back to full function (with some work on your part). If there is a more severe tear, the rehab process will be longer but again...no way of knowing this unless you have someone actually assess it. Even though you are physically active, an individualized rehab program to address issues with your ankle will make the recovery process go a lot better than just waiting for it to "get better". On top of that, once the ankle is assessed and you are starting to work on rehab, return to sport rarely starts once the ankle is 100%. It usually starts well before that point....a physio can help you determine how to gradually get yourself back out there and can assist you with necessary bracing / taping that may also make the transition easier.
Good Luck!