How do you know if it is skin irritation or purging?

Purging usually takes in the first month of using actives like acids or retinol/retinoids - usually purging can take up to 28 days (so called cell-turn over time, this period of time gets longer with age) and usually it looks like a break out. Skin irritation is nothing else than inflammation/redness that might look like rash, it can be bit painful or even your skin might start to peel

I usually only use soothing and calming products if my skin is irritated

How long have you been on retinol? Most ppl normally purge in the first 8 to 12 weeks, before it settles. Can be different for everyone of course. If your just starting retinol, I would back off other acids until your skin adjust. Start slow and on your off days really focus on soothing, hydrating repairing your skin barrier.

I agree with what's already been said. I can suggest a great calming product though.