Cook rice according to package instructions; set cooked rice aside.
Using a large bowl, add shrimp and teriyaki marinade; toss until well combined. Cover and refrigerate 1-2 hours. (Note: Do not marinade the shrimp longer than 2 hours or it will become mushy.)
Remove shrimp from marinade and set aside. (Note: Do not discard marinade!)
Stir the water and cornstarch into the leftover marinade; set cornstarch mixture aside.
Place a wok or large skillet over medium-high heat.
Once hot, add oil and sliced carrots; sauté, stirring occasionally, for 1 minute.
Add stir fry vegetables, snow peas, mushrooms and sesame oil; sauté, stirring occasionally, for 2-3 minutes.
Add shrimp; continue sauteing, stirring occasionally, for 3-5 minutes or until shrimp are pink and fully cooked.
Add marinade mixture (from above) and bring to a boil. Sauté, stirring occasionally, until sauce has thickened.
Serve over cooked rice. Top with toasted sesame seeds before serving.