Trying to avoid getting into any ethical discussion...
A VPN is unuseful for your scope, it would be sufficient to navigate in private mode (IE, Edge, FF, Chrome, Opera ... have this mode) to not leave traces of the PC you're browsing from... unless your parents are IT experts and sniff the data from outside the house. This would be the only case that a VPN might help... otherwise anything inside your house in not affected by the VPN.
The best way for them to check (and stop) would be easily through the Router Setting where (usually) you can log: traffic, data usage etc. without my kids even knew that! And with a good pwd nobody could change the router settings but me!
Again all these considerations based on the assumption that you are not the owner and payer for the DLS connection (despite being +18)...