Do I need to register for Self-Assessment if I've just become self-employed?

Yes, you need to register for Self-Assessment as soon as you start trading, and the deadline is 5 October following the end of the tax year in which you began (the tax year runs 6 April to 5 April). Registering gets you a Unique Taxpayer Reference (UTR) which you'll need to file your return. Miss this deadline and HMRC can charge a failure-to-notify penalty, so it's worth doing early even if your first return isn't due for a while.