It would be possible to double major in Nursing and Chemistry or Biology - but very difficult..and you will need to find a school that would allow you to do that. All colleges won't - even if they offer both of the degrees you're interested in. A nursing degree is quite challenging and requires lots of math and science to begin with. And I'm referring to a BS in Nursing. You can work as a nurse with just a 2-year degree... Make sure you understand what an RN - a registered nurse is. The RN refers to state.national licensure or certification - not the educational degree the person has. An RN could have completed a 2-year degree and taken and passed the RN licensure exam. And a RN could also be someone who has a 4-year Bachelor of Science in Nursing and then took and passed the RN licensure exam. The RN refers to the passing the nursing licensure exam. Also know that the industry is moving to toward POSSIBLY having all RN's obtain a Bachelor Degree in Nursing before they can sit for the licensure exam to become an RN. This MAY happen by 2020. But for now, you can still sit for the RN licensure exam even if you have a 2 year nursing degree.
Check out these links for more information about this.
Some places may also let you double major in Nursing and Pre-med - though not many. Any nursing degree requires Clinicals - and once you start your clinicals - working in different settings as a nurse while you learn - it's full time - so when would you have time to work on another degree program? Most schools will discourage a double degree in nursing and something else. Not many nursing double major in Nursing and something else. It's not common. Try to speak with people who DO what you want to do... talk to nurses... different kinds who have different degrees....and ask lots of questions. Consider volunteering at hospitals or clinics so you can see what they do and talk to them about their education. There's no better resource than that. Good luck.