You hold yourself to a higher standard.
Rightly or wrongly, you hold yourself to a higher standard when working for yourself. If your clients are happy with the work then you are happy with the work, but your clients generally don't have the same eye for design as you do.
We probably all believe (consciously or not) that our own website, logo, branding and anything we put out there to represent ourself should be the very best of our work.
You don't need a design, you need a brand.
As a freelance designer, you are branding yourself. Whether you are presenting yourself as person or as a company, it is still you. The branding will reflect on you as a designer and as a person. Figuring out who you are, as a designer and as a person, isn't something everyone is comfortable with. Even if you are comfortable with that, that doesn't make it easy to honestly represent that.
Your brand and design needs to be truthful to who you are. You could design the best looking website and logo but if in your heart you know it doesn't represent who you are, it won't feel right and you rightly won't be happy with it.
A brand isn't a design, it is an idea.
My advice—take a step back and find out who you are. Forget about a website design or anything that specific to begin with. Creating a brand is like telling a story, and that story is your story. A brand isn't a logo, it is an idea. Start basic—who are you? What food do you like? What music do you listen to? What is your work ethic? It all adds up to a big picture of you. From that story you build an image of yourself and build your brand around that.
From there your website and business cards and whatever else will come easy.