Shrimp Fajitas with Mushrooms and Corn

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1/2 teaspoon smoked paprika

2 teaspoons packed light brown sugar

1 1/2 teaspoons chili powder

1 1/2 teaspoons ground cumin

Kosher salt

1 1/2 pounds medium shrimp, peeled and deveined

Juice of 2 limes, plus wedges for serving

2 tablespoons extra-virgin olive oil, plus more for the grill

8 ounces shiitake mushrooms, sliced

4 ears of corn, kernels removed

1 poblano chile pepper, seeded and chopped

2 tablespoons unsalted butter

3 scallions, chopped

8 to 12 flour tortillas

Crumbled Cotija cheese, for topping