Problems with email alias (can’t send emails / being redirected to outlook 365?)

So I've recently set up an email alias to my main account that's affiliated with my graduate school (my graduate school forwarded all emails sent to that .edu email to our main address - in my case, my live.com email), however I've been having some issues with being able to send an email from that alias. When I create a new message, or reply to a message, sometimes my alias is in the drop down box, and sometimes it isn't, it's never consistent.

I thought that making that .edu address my primary alias might fix things. Instead, I can't login to my email account anymore (either my live.com address, or my .edu address) as I keep receiving a message to log out of my outlook 365 account. I have no idea what outlook 365 is, nor have I ever registered an email to outlook 365.

I managed to fix that, but now I'm stuck with my initial issue, that is, I can't send an email from my alias. I have no idea what triggers it to work, but on random days, it'll allow me to send emails from my .edu account, and on some days, that won't be an option.

Any help would be appreciated!