Got an account alert email asking me to sign in to my hotmail

Don't click anything in it. Most of these are phishing. Open your browser, type the Microsoft account address yourself, sign in, and look at Security > sign-in activity. If there's a real problem it'll be showing there. If there's nothing, delete the email. Look at the actual sender address too, the fake ones are usually not from a Microsoft domain at all. If you already typed your password into the link, change it straight away and turn on two-step verification.