I share my wifi with my brother. Recently I came to know he is sniffing on my browsing. Is there a way I can prevent him from sniffing on my browsing?
PS: I can't afford VPN.
Encrypt. VPN, ssl, https, etc. That's what they are for, to create secure channels within insecure environments.
HTTPS is an option for 'browsing'. Always make sure you are using the https version of sites instead of the http version. There are browser plug-ins that can help with that, too.
Challenge your assumption that you cannot afford VPNs, With a little knowledge, you can create your own.
Another potential solution is to find a used wifi router for free and use that to connect to your home's Internet connection. Set it up for yourself and don't tell your brother the password ...
In addition to Schroeder's good answer, I'd like to say that you can use the Tor browser bundle. Once on your system, just click the onion and you're browsing privately. Tor won't work for watching videos, but it's great for browsing. I've used it for browsing Facebook (and other sites) which works fine. Even if your brother wouldn't be spying you, Tor is great to ensure your privacy.
I recommend reading the documentation before use. It's important to understand that browsing is anonymous, but if you enter a form (e.g. your name) on a web site, obviously the web site gets your info. It sounds like just want browsing privacy, so this should be acceptable for you.
Also, regarding the trust issue with your brother: Don't forget that your brother might try to boot your computer when you're absent. Make sure none of the passwords of your important accounts (email, Facebook, etc.) are easy to guess.