Can you put awards from a project on your CV, if you had help with the project?
I commend you on taking ethical authorship seriously. Authorship requirements are not entirely clear, and customs may vary across academic disciplines and cultures.

I would include the awards on your resume/CV. Based on what you described, I doubt that you will ever have the legitimacy of your claim to authorship questioned, since you developed and executed a majority of the ideas for your project. Also, you are not trying to take credit for others ideas (you are very clear and forthcoming about who thought of/did what), you are just saying you won awards, which you did.

There are many articles in peer-reviewed journals on authorship ethics. For example, this article in Nature.

Nature also published an article on a physics paper with >5,000 authors.