Facebook still often locking me out after removing trojans, changing passwords and reformatting PC?

2 months back, I picked up 2 trojans on my laptop. Hackers had accessed Google profiles on the device, and through that my Facebook account.

I downloaded Bitdefender which removed the trojans. Since then I have moved everything (incl Facebook) over to a new Google account, changed paswords, formatted my laptop and phone. Bitdefender comes up clean every time and I'm not getting any security flags from Google or any of my other accounts.

During the initial hack, when my Facebook was compromised, I lost access to our charity's Facebook page, leaving only the president with admin access.

However, since all of this, Facebook periodically flags up that they think someone has gained access to my account and asks me to verify my identity. I've considered that it could just be Facebook getting a bit twitchy given that during the first hack they'd changed my profile pic to the flag of a known terror group.

However, one of these occasions happened a few days after it became apparent that hackers had taken over the charity's Facebook Page and had begun posting dodgy looking product posts in foreign languages.

In theory I never had access so it couldn't have been through mine, but it seems a strange coincidence.

I have two-factor set up on Google and Facebook so I'm so stuck for ideas here on what's happening (if anything) and how to finally feel safe online again. I'm starting a new job in a few days and I don't want the same thing to happen to them.

Sorry this was so lengthy but please help if you can.