aspiringChemE

I am a current junior going for a BS chem degree at an average university. I have a 3.8 and the grad school advisor at my school is simply telling me I should not worry about getting in somewhere with funding. Is this true? I am certainly still worried about the possibility of this transition. I have a year of undergrad research experience, but it is in organic chemistry. I have not taken the GRE yet, but it should not be a thing that hinders me. I would appreciate any sound advice from anyone who has seen this transition. Thank you.