Bring a large pot of salted water to a rolling boil. Add the rotini and cook according to package directions until al dente, 9 to 11 minutes. Drain in a colander and rinse under cold running water until cool. Shake off excess water and set aside in a large mixing bowl.
Pat the shrimp dry with a paper towel. Heat olive oil in a large skillet or the stockpot over medium-high heat. Season with half the Old Bay, salt, and pepper. Cook for 2 to 3 minutes per side until opaque pink and curled. Transfer to a plate, cool for 5-10 minutes, then refrigerate until fully chilled. Roughly chop any large shrimp, leaving smaller ones whole.
Dice the celery, red bell pepper, and red onion into small, even pieces. Thaw the peas under cool running water and pat dry. Zest the lemon before juicing it, then set both aside separately. Chop the fresh dill if using.
In a small mixing bowl, whisk together the mayonnaise, lemon juice, lemon zest, chopped dill, and remaining Old Bay seasoning until smooth. Taste and adjust with salt and pepper.
Add the chilled shrimp, celery, red bell pepper, red onion, and peas to the bowl with the cooled pasta. Pour the dressing over the top and fold gently with a large spoon or spatula until evenly coated. Taste and adjust seasoning as needed.
Cover the bowl tightly or transfer to an airtight storage container. Refrigerate for at least 30 minutes before serving to let the flavors settle. Give it a gentle stir right before serving.