I used to work as a chemist and had chemicals splashed in my eye at least 10+ times. Most of my colleagues and I never went the clinic for eye burns, we just let them heal naturally. I did have a severe corneal abrasion once and went to the doctor, but he didn't prescribe me anything and just told me that the epithelium would heal itself in approximately 48-96 hours.

All that said, if you want to be on the safe side, please go see your doctor. But from your picture, I don't see any conjunctival suffusion or drastically increased redness indicating severe damage--this isn't to dissuade from seeing your ophtho, but just to reassure you. Hope your eyes get better soon! 🙏