Firstly, this sentence must include a proper conjunction between "week" and "I" because a comma alone does not work in this case. You could use the word "but" after the comma, a different conjunction after the comma, or use a semicolon instead of a comma. An easy way to determine this is to check if each part of the sentence could be its own sentence independently. In this example "I was not feeling well last week." and "I am okay this week." can also be independent sentences. Therefore, to use them both in one sentence you must include a comma with a conjunction or a semicolon.
In the context of your sentence, the word "this" is being used as an adjective. Therefore, it must have a noun or pronoun which it describes. The second sentence is grammatically incorrect because it cannot describe the previously used "week" because it is in a separate clause and "last week" must be stated separately from "this week". Therefore, you must again say "this week" since it is needed be described by the adjective and to clarify what you are talking about.