Isaiah Berlin's concept of "positive" liberty and "negative" liberty, as set out in his essay, "Two Concepts of Liberty," is not what you think. Specifically, the simplistic idea in which "positive liberty" is "freedom to do something or get something" and "negative liberty" is "freedom from being legally prevented from doing something," is simply not Isaiah Berlin's definition of the two ideas.
Positive liberty and negative liberty, according to Berlin, are not exactly different kinds of liberty. Instead, they are different ways of thinking that each attempt to address the whole concept of liberty. These two ways of thinking often, but not always, reach similar conclusions.
The freedom which consists in being one's own master [positive liberty], and the freedom which consists in not being prevented from choosing as I do by other men [negative liberty], may, on the face of it, seem concepts at no great logical distance from each other--no more than negative and positive ways of saying much the same thing. Yet the 'positive' and 'negative' notions of freedom historically developed in divergent directions not always by logically reputable steps, until, in the end, they came into direct conflict with each other.
In Berlin's essay, he introduces "negative" liberty as a school of thought in which liberty is the freedom to act as you wish, as long as you are not interfering too much with the freedoms of others to act as they wish. According to the negative liberty school of thought, liberty is the freedom to swing your fist as long as it doesn't contact someone else's nose. This is not too far off from what you said.
He introduces "positive" liberty, however, in a very different manner. Isaiah Berlin's positive liberty is a school of thought in which freedom is the ability to act only as a wise, rational person would act. According to Berlin's positive liberty, if you are ruled by alcoholism and drink to excess, you are not free, just the same as if you are bound in chains.
Politically, the negative liberty school of thought would suggest laws that just stop people from directly hurting each other. The positive liberty school of thought would also suggest more paternalistic laws that mandate people to act in a "wise" manner, such as laws against public drunkenness or drug use.