Perhaps the fasting was the trigger for the Acne and not the sunscreen - as fasting will release toxins and if they cannot be eliminated fast enough through the liver and bowels the skin will show conditions as it's the largest elimination organ of the body.
The sunscreen then probably prevented toxins from 'venting' from your skin, essentially trapping toxins under the surface to then develop into the really large spots you describe.
(I've had those in the past - they don't develop a head sometimes and remain a large, painful red lump for weeks).
Then taking the Antibiotics for Acne could have impaired your gut bacteria - and THAT is one imbalance that many people have with acne. I went the Antibiotic route in my youth to clear Acne and it got way worse as my bowel ecology became redundant!
An intensive probiotic course, over and over is something worth trying.
Get the best quality you can - or like as Shark suggests - a Fecal Transplant from a very healthy donor.
I had acne since hormones started at age 12 - it never went until hormones went completely wild and out of whack 2 yrs ago! So something i am thankful for i guess ;-) So for me there is a hormonal imbalance that made acne worse - namely very high testosterone coupled with estrogen and low progesterone.
In men it seems that high T levels alone can increase acne and also skin oiliness.
Wish you huge luck on your healing journey...you'll figure out a good routine and will progress, from the sounds of it you're putting in loads of effort - don't give up, you'll get there!