Hi Catherine,
There is a lot of really good support documentation to help you through this problem. I especially enjoyed the seminars given by the two Laurens from ESRI product development (let me know if you can't find them via Google, they do a great one on analysing Medicare spending and 911 call volumes that would probably help you a lot).
What I learnt about your question from this is:
1. You can't do a GWR or OLS on point data unless the values of the points are different, i.e. the values that you will use as your response variable must be different - you would have to aggregate your data (they show how to do this in the tutorials). Since you say you ran an OLS on your point data already, it seems that your values do already have a variety of values
2. You cannot successfully run GWR until you have found a properly specified model in OLS - which you can do using Exploratory Regression. Again, they show how to do this comprehensively in the tutorials
3. Until your model in OLS passes all the 6 checks that are mentioned in the tutorials, you should not run GWR UNLESS you are certain that the spatial autocorrelation is because of regional variation or non-stationarity. In Exploratory Regression you should keep looking for additional SPATIAL explanatory variables (map the std residuals by running the same variables in OLS to get clues of what spatial variables may still be missing) until your spatial autocorrelation is gone. Then run GWR with these variables, omitting the spatial variables, which are automatically accounted for by GWR.
All of this is in the tutorials, but hopefully this helps. It really helped me a lot to go through the tutorial material.
Kind regards
