How do I stop this pawn storm?

Black does not have to castle.  The Black King can remain in the center behind the strong pawn formation at d6, e6, f7 (see many  games especially 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. g4)

I am not very familiar with this sicilian variation
Pretty sure I would have played Nc6xNd4 and/or Bb4
This gets me to 10. ... I would have gone ... Na5,
getting the half-open file working for me, with a Nc4 in mind.

11. h5 was dumb compared to f4, forcing knight back to g6.
This gave you a second chance: 11. ... Na5 12. Bf4 d6
13. ... you really do not want Nf7, ... NxN and ... Nc6
14. ... Ne7, you really need to get the c3 threats working.
16. ... You have Nxg5 and a big wood chop has ... Qf4

                                                                 ________________________

6.g4 is the Keres Attack.  There is also the Perenyi attack.  With 6.Bg5 White is throwing everything at Black's position including the kitchen sink.  The Bulwark pawn formation (d6, e6, f7) where the Black King stays in safety no matter what attacks White throws at his position.  There is no need for Black to waste tempii castling and making pawn and piece adjustments.

If youre going to play an opening you dont understand, a good start would be to learn how to play the opening.

Let’s take a look at when it makes sense to castle opposite sides and when it doesn't.

You should castle on the opposite side when at least one of the following factors is true:

1. When you are up in development and your opponent has already castled, you should consider castling in the opposite side. That way you will have a clear game plan and will also be able to capitalize on your development advantage.
2. When you have a damaged pawn structure (doubled paws, missing pawns, far advanced pawns, etc.) on one of the sides you should consider castling on the other side.
3. When opponent’s pieces are especially active on one side of the board, it is usually best to castle on the opposite side.
4. If you want to complicate the game you may consider this option. That may be true if you must play for a win due to a tournament situation, when the draw is not enough. Also that maybe done when you're playing against a stronger opponent, who is much better in simple/technical positions. That maybe your best bet.

You should not castle on the opposite sides when at least one of the following factors in true:

1. When you are behind in development and you need extra time to develop your pieces, it is usually not a good idea to give your opponent a straight forward way of launching an attack.
2. When the opponent’s pawns are advanced towards the side you’re about to castle, it is not a good idea to castle there (especially if the opponent’s king is castled on the opposite side). It will just give him a positional edge in the attack.
3. When there are open/semi-open files in-front of the side you’re about to castle, you should probably reconsider your decision to castle there (especially if your opponent has castled on the other side). That will give him more attacking possibilities, such as rook lifts, various sacrifices, doubling of pieces on the file, etc.
4. If you playing against a weaker opponent you may want to avoid castling opposite sides, in order to avoid sharp game and keep everything under control.

Note: These are general rules, not laws, meaning that there are always exceptions to them. When you’re making a decision what side to castle you should always take your time and evaluate all “pros” and “cons” and base your decision upon your own analysis. This is a very important decision. It pretty much dictates which way the game will continue. Take your time and think twice.

during the pawn storm you better not castling if you wanted it to because that will be dangerous

your opponent is too strong

you cant  stop it

Why did you castle directly in front of the pawn storm. You could've kept the king in the centre. Also when your opponent pawns are marching to your king, you are supposed to strike in/dominate the centre and activate your pieces to stop/counter the attack. Also you castled opposite when opponent was ahead in development as well and already began to gain space with pawns

Castle queenside.

Hello!