The phrase “gotten me interested” means that something has aroused one's curiosity or captured one's attention. A synonym for this could be “piqued my interest”. “Pique” means to arouse or excite, so “piqued my interest” implies that something has sparked one's curiosity or fascination. For example, “The new book on ancient civilizations has piqued my interest and I can't wait to read it.”
Another synonym is “captivated my attention”. “Captivate” means to attract and hold the attention of someone. When something has captivated your attention, it has completely engrossed you and made you want to know more. For instance, “The beautiful scenery on our vacation captivated my attention and I took countless pictures.”
“aroused my curiosity” is also a good synonym. It clearly states that something has awakened one's desire to know or explore. For example, “The mysterious noise in the attic aroused my curiosity and I decided to investigate.”
All of these synonyms for “gotten me interested” express the idea of being intrigued or fascinated by something, and they can be used to add variety and color to your language.