Well I am a postgrad student taking my last few prereqs before nursing school. I have taken both Chem I & II, both courses were for science majors.
I would agree that you should have algebra under your belt before taking chemistry. Chemistry is very quantitative in nature and a LOT of the work we did was solving problems, problems, and more problems.
Here is the thing though, in TX, the nursing programs usually allow you take chemistry courses geared towards non-science majors or for people who are going into allied health careers. I guess you could say that compared to chemistry courses for science majors or for those going into medical school, it is supposed to be easier.
You REALLY need to go speak, in person, to your future chem professors and get their opinion on it. If they really stress algebra as important, then you want to be comfortable in it before class starts. You do not want to have to learn chem and math at the same time! Good luck and study hard, don't let a fear of numbers erase your dreams.
"Obstacles are those frightening things you see when you take your eyes off the goal."-Hannah Moore