I did the exact same thing you did. Go out and buy at least 15qts. of the cheapest oil you can find. Enough for at least 5 oil changes or until it clears up. Put in about 3 qts at at time & crank it up so that it circulates in the engine. Drain. Repeat until the oil is not milky & clears up. When the oil finally comes out clear, then put in the good stuff. There ain't no sense in buyin' the expensive oil just to run it through to clean the motor out. You will need to change the filter a time or three during the flush process. Do not let the water set in your motor very long. It could cause severe damage. Get it out asap. Other than you should be fine. It is a Honda, what are you worried about.