Firstly, do your lips still peel regularly? I think the dryness and 'paper' sensation you felt at first could be due to excessive dead skin buildup (this could be due to lip-licking syndrome or too much use of lipbalms).
The 'numbness' and purple/ dark purple spots are probably due to damage of tiny blood vessels in your lips, causing a buildup of low-oxygenated blood.
Your current sensation with the itchy and sometimes burning sensation is very likely due to inflammation of the lips (immune system secretes histamine, which dilates blood vessels and causes an 'itchy' feeling). Inflammation of the lips is termed cheilitis.