Has black’s moyo already given them an advantage
Your big mistake was your slack move at 12. It's a bit scary to have Black make two shimaris. The reason he shouldn't have done this is that his two stones in the bottom left corner were left stranded. You should have played 12 one or two points to the left of 13, and chased these stones. This would have given you an initiative that would have more than compensated for the two shimaris. Assuming that you play as well as Black from this point, you should win the game.

When Black got to play 13, he fixed his main weakness AND limited value of your shimari in the lower right, killing two birds with one stone. Now it is your stone at 12 that is in the middle of Black's influence. The 13-14 exchange was all in Black's favor. Ditto for the 15-16 exchange, after he solidified with 17. Your 18 was basically forced, but the 18-19 exchange was again in Black's favor. After you played 20 and he played 21, your (ultimate) response at 26 was too little too late. You have fallen one step behind, all because of move 12.

You are about 20 points behind on the board, although komi will reduce Black's lead to less than 15. By falling a move behind at 12, you, in essence gave Black the equivalent of a "two stone" handicap instead of just playing White. You will probably lose this game, even with komi.

I've noticed a pattern that will likely cause you to lose as White. You "follow" Black around, playing 12 in response to 11, 14 in response to 13, 16 in response to 15, 26 in response to 21, etc. This gives Black the advantage of every exchange, and creates the Black moyo pattern you referred to. (You also have a bunch of moyos, but they are much smaller.)

Komi can offset only one such exchange, so you need to find ways to break the pattern (or punish Black for improperly doing so). Moves 8 and 10 were a good idea, because you had sente in that part of the board. Black needed to play J3 (give or take), and then you could have grabbed the kakari at C15 for 12.

The shimari at 11 was big; it's worth about 1.5 stones because of the synergy with the rest of the position. The pincer (or protective move) at J3 was even bigger, because it affected the fate of two stones. That is, your pincer would either have captured them, or more likely, yielded an equivalent benefit, that would have put you ahead (2>1.5).