Is Tunnel Bear not going to work with my Chromebook?
Tunnel bear will probably work. However, as it was recently sold to McAfee (https://techcrunch.com/2018/03/08/mcafee-acquires-vpn-company-tunnelbear/), I suggest that you look for other VPN.
Proton mail has a better VPN free version https://protonvpn.com/free-vpn
You can read how to set a vpn on your Chromebook
https://www.pcmag.com/article/361469/how-to-set-up-a-vpn-on-a-chromebook
Broadly speaking, there are three ways to get your Chromebook protected by a VPN: You can use a Chrome browser extension, use an Android app, or manually configure the client in Chrome OS to use the VPN of your choice. Surprisingly, going the Android route is probably your best option. Each method, however, has potential drawbacks, ranging from a lack of support to a lack of documentation, as I'll explain.