I would recommend buying a domain name, they are cheap and you can get free hosting or really cheap hosting somewhere.
tinyurl or other services are OK, but my biggest fear is that if they suspend your account they then take over your links and you are out all the hard work you did and you can't do anything about it.
I would buy a good link management software. Try
Manage Affiliate Links Anyhow, it protects your links against link thieves and cloaks your links. The best feature is that it will redirect dead, expired, or broken links to a backup link that you choose. Very handy if you run lots of campaigns.
They also have a version where you don't need a domain or website, you use their site with their software but I think its by invitation only. Try emailing them if you are interested.