Most financial advisors will say, yes. If you are self-employed, you are, in a sense, your own business or a sole proprietor and you should keep your personal and business transactions separate. Keeping your accounts separate helps with taxes and helps give you a clearer view of your revenue and business expenses. You may benefit from incorporating and obtaining a "doing business as" (DBA) and a business tax identification number too.
Other reasons to have a separate business account, it may help you to:
Look professional
Protect your personal identity
Acquire funding
Manage business expenses better
Keep your personal transactions private
Process credit card transactions (with processing)