From sole proprietor to LLC
Technically you could form a new LLC and try to obtain EIN and Sales Tax ID for this new entity, which would be an entity separate from yourself.
With that being said I want to clarify one point - you can't really "close" a sole proprietorship in a sense that its not a separate entity - its pretty much you. So if you owe taxes you would have to resolve it as soon as possible, simply because the authorities you owe your taxes to might choose not to issue your LLC the right permits (EIN, Sales Tax ID, etc.) if they manage to cross-reference the two companies.
Whether they do it or not is another question, but the risk does indeed exist.