"Nicht" is the last word (I think this is what you meant) because so far we've only seen it placed right after the verb ("Ich bin nicht normal" > "I'm not normal", etc) since that is the part of the sentence it is negating.
In this case, "Ich schwimme" = "I swim", and "Ich schwimme nicht" = "I do not swim"
In this instance, it is referring to not doing it, rather being unable to. I know people who are strong swimmers but absolutely hate it, so don't. Another example: "I don't drive"—I am able, and legally licensed to drive, but I don't (for various reasons).
I got caught out on a similar thing in the last lesson with "You see the insect" which is technically right, but so uncommon in English that I automatically went for "You CAN see the insect" which would be different.
Hope that helps. Sorry it was so long.