London IB Internship application with zero experience - is it possible?

Hey, so I have a problem. I'm a UK student at a top-target (Cambridge) entering my second (the penultimate) year. I've been interested in IB since entering first year - or in other words I'm pretty sure I can give up two-to-three years of my life and live them in total misery. I managed to get a spring week at a BB last year. However, I became really sick halfway through. I'm not allowed to put it on my CV or talk about it. I then compensated for it by working my ass off for my first year exams and managed to get a First (relatively few on my course get it).

I've had a rough summer (with no internship) and I haven't focused on applying for internships for next summer. It's late, so I'm applying somewhat widely (equity advisory (which I really like the sound of), AM, REPE, tech stuff). But I'm facing some problems - I have pretty much nothing to put on my CV or cover letter. I didn't do any of the resume-padding student clubs bullshit, and I can't put my spring week experience on my CV. So I have jack shit to put down as relevant experience.

All I have is my first year exam result as well as, some random retail jobs, volunteering at a legal charity, and tutoring. I won't put those down. I have one thing which I might now have to make the focal point of my application though, and here is where my main question lies. For a couple of years I did some random entrepreneurship. I managed to make a few thousand dollars doing it, and I learned a huge amount. I did everything from originating sales to setting up billing systems. All indepdently from scratch. I have proof in the form of billing emails and other stuff.

So, because this is all I have, would it be a good idea to just make it the focal point of my application? Or will I just be dinged because I don't actually have any legitimate experience (I know I should have hustled to get more internships, but im only entering my second year). Should I just give up on IB/finance in general given that I've messed up? I legitimately believe that my experience here is way more meaningful than any of these bullshit first year useless PWM internships that everyone else has. Is just pushing the self-starter/I can learn a lot angle a good idea? Do I have a shot at BBs?

Anyway, sorry for the incoherent post. Short version - I have literally zero relevant experience, do I have a shot at getting any IB Summer Analyst positions? Thanks for any help.