While playing a rapid game, I accidentally dropped my water bottle on the chessboard, which made many pieces fall. I don't remember the initial position, and neither does my opponent. Should we play the game again, or is there any other rule about such cases?
There are two articles in the FIDE Laws of Chess which cover this, 7.4 and 7.1.
7.4.1 If a player displaces one or more pieces, he shall re-establish the correct position in his own time.
7.4.2 If necessary, either the player or his opponent shall stop the chessclock and ask for the arbiter’s assistance.
7.4.3 The arbiter may penalise the player who displaced the pieces.
So, first of all you should expect some kind of time penalty for what you did. Note that it doesn't make much difference that it wasn't your fault in the sense that you may not have done it deliberately.
Playing in a tournament some years ago I saw something similar happen. One player stood up and his leg caught the tablecloth pulling it, displacing a glass of water and the board which also got soaked. The arbiter came running over and the first thing he did was add two minutes to the opponent's time because of the disturbance caused. This was at standard time controls so the moves were recorded but in any case both players were of a sufficient level to be able to recall the position exactly.
7.1 If an irregularity occurs and the pieces have to be restored to a previous position, the arbiter shall use his best judgement to determine the times to be shown on the chessclock. This includes the right not to change the clock times. He shall also, if necessary, adjust the clock’s move-counter.
So, if neither of you can recall the exact position immediately prior to your accident then you should try and agree on a previous position. Unless you are both complete beginners you are likely to at least remember the opening.
If it was a social game, the polite thing to do might be to apologise and concede the match, and offer to forfeit to your opponent.
Politely, your opponent did not cause this situation and should not be at a disadvantage. If you can't agree on where the pieces were, allow their memory to prevail.
If time allows, you could start the game from the beginning, and you'll find its relatively easy to play through the same game quickly to catch up. Humans tend to remember sequential moves a lot better in order (eg, finding your keys by stepping forward through the day rather than backward.)
Of course if this was a competition then the above answers are irrelevant.
Separately, consider a coozy or some other way to add grip to your water bottle, or develop a habit to keep the bottle below the level of the table, and turn away from the board to sip.