Heat a large oven-safe skillet with oil over medium-high heat. Add zucchini and saute until very tender and reduced in size, 7 to 8 minutes. (Note: If the pan starts to look dry while the zucchini is cooking, add some water as needed.)
To zucchini, add garlic, cumin, and some salt and saute until fragrant ~1 minute more.
Move zucchini off to one side of the pan and add shrimp to the other side. Cook shrimp on one side for ~2 minutes to get it started cooking. Stir everything together and continue cooking until shrimp are nearly cooked through, ~2 minutes more.
Pour sauce and corn into the pan and stir to combine.
When sauce begins to simmer, gently fold in tortillas. Top enchiladas with cheese.
Transfer pan to broiler and broil until cheese is melted, 4 to 5 minutes. (Be careful when removing the pan - the handle will be very hot.)
Let enchiladas cool slightly and then serve with sour cream on top and lime wedges for squeezing over top. Enjoy!