Ok this issue is quite complex and requires lengthy explains so hopefully, you can understand the overall issue. So bear with me for a second.
Since you said you didn't find any organization in the Active directory, I suspect because of these reasons:
- You probably have only signed up for MS Team personal account in the past.
- You have been removed from other organizations as members.
I'd like to let you when it comes to MS Team free, I'd like to let you know there are 2 types of accounts:
- MS Team free personal account.
- MS Team free organization account.
Please note, those 2 accounts are not the same. They are indeed different. MS Team personal account is not registered in the active directory, However, MS Team free organization account does. Please note, in the active directory, only organizations can be listed.
As of the moment, MS Team free personal account can only be accessed via MS Team online (web browser) on the computer and via MS Team mobile app by clicking the personal account on the left (see screenshot below). 
if you want to access MS Team free personal account, please visit this link:
https://teams.live.com/
Having said that, MS Team free personal life account is targeted to be available on the MS Team desktop app in February 2021 but the current status is still under development: https://www.microsoft.com/en-us/microsoft-365/r...
In order to access the MS Team free organization account via a web browser, you need to go to http://teams.microsoft.com which is problematic to you but I will explain in a minute why so.
The reason why you don't see TIC, PB Associates, isavia in the active directory because you have no longer member of that organization. Simply you have been removed from the organizations. The reason why you still see those organizations on the mobile app probably because MS Team mobile app still stores the old cache on your mobile phone. Remove the account cache, uninstalling & reinstalling the mobile app may help.
In order to be able to access http://teams.microsoft.com you need an MS Team organization account which you don't have now since you have not signed up for the MS Team free organization account and also you have been removed from other organization as well so therefore without organization account it's not possible for you to visit http://teams.microsoft.com.
So in this case what you need to do instead is, signing up for the MS Team free organization account. Please refer to the following article: https://support.microsoft.com/en-us/office/sign...
By the time I'm writing this message, only the MS Team organization account can access the MS Team desktop app, it will be available for MS Team free personal account in the next few weeks or so, please stay tuned. Please note, if you have successfully created the MS Team free organization account and then you are trying to access the MS Team desktop app but experiencing a loading screen issue that's 2 different issues from what we are talking about here.
The loading screen issue seems to be an intermittent issue that you may be experiencing due to the network overload or maybe a recent rapid growth of Teams service usages that led to system overload and service degradation.
Please let me know if you have difficulty signing up for MS Team free organization account, I will assist you with further assistance.
Kind Regards