Yes, you can use any type of battery that is compatible with the Sony Vaio SVE151A11W/SVE15228CGP. However, it is important to note that different types of batteries can have different levels of performance and life span. To ensure that you get the best performance and life span out of your new battery, it is strongly recommended that you purchase an original Sony battery. If you are looking for a more affordable option, you can also look into compatible batteries from third-party manufacturers.
As for your issue with the battery life, it is possible that your laptop is using more power than it should be. Make sure that you are running the latest version of the operating system, as well as any other software, to ensure that you are not using too much power. Additionally, you can check your laptop's power settings and adjust them for optimal performance.