An Android spyware app runs on the Android operating system, you didn't specify what operating system your laptop is running so presumably it's running Linux, OS X/MacOS, or Windows, so no, if you're specifically asking about a spyware app it cannot install itself on a different operating system.
But there is a much more likely problem that is not tied to any specific operating system or device -- if your email account or some online service account (i.e. Facebook, Twitter, Instagram, etc.) is compromised in some way, than that will be a more extensive problem that's not specific to your phone or your laptop but your online presence. Use different and safe passwords for each online account, and when available two-factor account logins.