No, you won't be automatically charged at the end of the free trial. You will be charged only if you upgrade to a paid plan.
At the end of the free trial, if you have not upgraded to a paid plan your access to your stats and management tools will be closed automatically. You will still be able to login to your account to access our free resources and the Plans & Pricing page, from which you can purchase a plan.
NB: As of the 25th September 2018, all new Instagram profiles added to Iconosquare must be Business Profiles. This includes free trials and adding new profiles to your paid plan. Further to this, as of the 23rd October, use of Iconosquare will be entirely restricted to Business Profiles. So if you have a personal account that you'd like to convert to a Business Profile so that you can add it to Iconosquare, you can learn how to do that here!