Cutting Out Sugar (?) (Bad skin)

So I started on here almost 2 months ago, went from 130lbs to 125lbs in the first month and haven't changed since then. Aiming for 118lbs (Where I was less than a year ago, I'm 5'6). I'm trying to eat smaller portions and I've re-joined a gym doing short bursts of cardio, HIIT routines, and strength training (trying to get fit so I can climb better). While it's only a 5lb loss, I've noticed I have a smaller waist and hips, and I can feel my abs again (although they're not visible yet).

However, since starting to exercise again I've got spots all over my back.

I've always had spots, not quite at acne-level, but just many many white and black heads all over my face, back, shoulders and chest. I'm 23, had bad skin since about 12, and got my first spot aged 10. In the past few years my spots have gone from my body (mostly) but now they're back!

I've tried every skincare regime possible over the past decade (!), including from my doctor, so I'm not looking for skincare advice.

What I really need is advice on my diet. I love chocolate, fruit, cake, yoghurts, crisps, more chocolate, sugar in my tea, hot chocolate, ...you get the idea. My diary is open I think (and terrible), although I haven't logged the past few days (moving house).

I know this is bad for my skin but I also know I don't have the willpower to cut everything out at once. So advice please, what have other people done? Did you cut out one particular food? Did you gradually reduce to no sugar at all? What about salty or fatty foods etc? I've recently moved too so it's the perfect time to re-assess my eating and cooking habits.

My spots also go down when I don't do cardio, though I'm not sure what this is due to. I shower straight afterwards and use acne body wash.

Thank you!