Will nicotine stay in my blood system for more than 24 hours?

Kind of: Nicotine has a metabolite cotinine, which stays in the urine for at least 2 weeks.

Yes: “When someone stops using tobacco and nicotine products, it can take more than two weeks for the blood level of cotinine to drop to the level that a non-tobacco user would have and several weeks more for the urine level to decrease to a very low concentration.” REF: http://labtestsonline.org/understanding/analytes/nicotine/tab/test/