I suspect that the servers of people you're trying to send new mail to have got spam filters in place that are identifying your mail as spam. That will either be because they block all Hotmail addresses (as some business email services now do) or because your IP address has become associated with spam. (The filter will allow your
replies through because the headers will show them as such).
If (like most people) you've got a 'dynamic' (rather than 'static') IP address, the first thing to do is to change it. That's hardly difficult; you simply disconnect your router from your phone line, wait a few moments and then reconnect it. Go here, both before and after disconnecting/reconnecting your router, to confirm that your IP address really has changed:
http://whatismyipaddress.com/
If the problem has arisen (as it may well have done) because your current IP address is one previously used by a spammer, that will probably be all that you need to do. However I also suggest contacting someone who has recently failed to receive an email from you and asking them to access their email account using webmail (i.e. NOT via an email client such as Outlook or Thunderbird). Ask them to look for a folder called 'Bulk', 'Junk' or something similar. In it they'll find everything which their email provider has classified as spam. I strongly suspect that your missing email will be in there; if so, the recipient should look for an option to label the email as 'Not spam').
If you really get stuck, create an email account with a different provider, such as GMX:
www.gmx.co.uk
Then use the 'mail collector' function to forward all mail sent to your Hotmail address to your new GMX one.
Chris