I'm sorry about the issue. Have you tried anything?
What happens when you try to access the problematic hotmail email address at the hotmail.com website? Is there any error or message?
Is your iPhone asking for your Apple ID account password? Or is it something else?
Is your iPhone currently able to receive text messages fine?
Do you also have a windows xp, vista, or 7, or 8, 10 computer, or a mac computer?
Please type at the box below, then click on the Send button below to communicate with me, so I can help. Thank you,