Bitcoin runs on a public blockchain. People will always be able to track your address.
But when I send the money to my cousin's wallet, can they follow it there, or can they just see how much I have at any given moment?
Everyone can see how much bitcoin every address owns at any given time. If you send from A to B, this will reflect on the blockchain and this will be trackable. People will not know the identity (name etc.) of the address owner, unless u have written it somewhere online and ur name can be connected to the address.