How can I get my email from outlook forwarded to my mobile?

We might be able to further help if we know what phone it is that you use?

Also, would you be open to altering your email client?

Most US cell phones can receive text messages from email.
http://www.makeuseof.com/tag/email-to-sms/

You could forward all messages. But text’s 160-character limit means messages are broken into multiple short texts.

I don’t think you can have outlook forward your email. Outlook actually receives email from the web so I imagine you’ll have to go to your email server (gmail, yahoo, etc.) and get the incoming and outgoing mail server credentials and put those into your phone.

Outlook can forward messages, or send a short text alert about them.
You do need the computer and Outlook up and running to do it.

About managing messages with rules
Rules fall into two general categories: notification and organization. Notification rules alert you in some way when you receive a particular message. For example, you can create a rule that automatically sends an e-mail message to your mobile telephone when you receive a message from a family member.

Alternatively, depending on your email provider (Gmail,Yahoo, work, etc), you may be able to set up forwarding or alerts on their email server, your personal computer does not do the work. For example, Gmail filters can forward mail based on sender, subject and/or key words.

If there is a webmail server associated with your e-mail account, you may be able to browse there if your phone can access the Internet.