You need to add alcohol to your plan. There are a lot of stories about people dying after they get drunk and accidentally tumble into water where they drown. Just read
here about
tragic student drownings. Sounds pretty good right? Alcohol also numbs you a little and will making drowning easier. That's a much better narrative than the murder one you have planned.
So one possible plan would be:
1. Buy an excessive amount booze, the heavier the bottles the better, you can put them in a backpack which will help you sink.
2. Get hammered, remember to put empty bottles in backpack
3. Find a suitable body of water. Take a nice stroll along it.
4. Slip and drown
There u go. From someone who also cares about their image after they die.
edit: actually empty bottles float haha, just put something that's heavy and inconspicuous in your backpack. Some of your books probably weigh the same as bricks