All information that you can see via our web-interface was also recorded in bitshares blockchain. This info is public and any person can view it, he don't need to be logged in to make this. To check this page, you don't need to be logged in too.
To check your balance you need to put into the following link your account name and follow it (copy and paste this link into address bar in your browser, write your account name instead of 'example1' and press 'enter' button) -https://openledger.io/account/example1/overview/
Please, use only lowercase letters!
You will see your account page.
You can see how many coins you have, how much does each 1 coin cost in BTS ( you can change currency in settings, if you want to see price in another currency), 24-hours price changing on our platform, value in BTS ( this is changing in settings too). Also you can go to exchange and check market of each coin.