Session storage security

I'm using a parse backend for my web app which uses the JavaScript API. I've currently got a log in page which redirects to another web page which allows data that's stored in the backend to be viewed.

Once I redirect to the page after logging in though I'm no longer logged in, I've come up with what looks like a solution but I'm not quite sure.

I've considered simply using a login page, storing the username and password in sessionStorage and then once the new page loads, basically logging back in with those credentials. This seems somewhat cumbersome though and I'm worried about the security implications involved with storing this kind of information in session storage.

I've read of people using session tokens though I'm only new to web development and I'm unsure of how to go about this or if it's the right way to go.