You need to separate last week into two words. Sorry to hear that you have been sick for the last two weeks. If this is an exam question, you need since because of the time duration. I have not eaten since yesterday. From denotes distance or location as I am not from this region. I am far from home From can be used with time as the meeting will take place from one until four. The time is not a duration. The phrase "from time to time" is likewise not a duration.

I have been sick since last week.

are well now ? you were sick because you made a grammatical mistake !