Yes is the short answer. You certainly must sign up for self-assessment with HMRC if you earned more than £1,000 through self-employment. Once you register for self-assessment, you will be given a Unique Taxpayer Reference as proof that you are a self-employed taxpayer. You will also have to pay National Insurance contribution payments which will go towards the state benefits and state pension you can receive in future years.
It is possible to be employed in a PAYE job and to also work as a sole trader, and even though you might pay tax through your job (PAYE), you will still need to register the ‘trade’ for self-assessment and declare both sets of income to HMRC in your annual Income Tax Return.