Bisphenol A is an ingredient in hard, glasslike polycarbonate plastic that's used for some kinds of bottles. It's used in the plastic resin that lines tin cans. It's also found in plastic food containers, CDs, dental sealants and toys. Plastic food containers marked on the bottom with the recycling label No. 7 may contain bisphenol A. Plastics with the recycling labels No. 1, No. 2 and No. 4 do not contain bisphenol A. Dangers include neurological or behavioral reactions ...but I don't think it causes an immediate reaction like this ...

What is the recycling number/ grade of plastic listed on the bottom of these items?

I have this same problem when I drink from some plastic bottles. I get dry stingy lips which go red, and then eventually crack.
Most lip balms do not help. The only thing I could find to sooth the redness was blistex cream for coldsores. This was an expensive remidee. No doctor is able to diagnose my problem and as it is not life threatening I find that they dont take my complaint seriously. The pharmasist then gave me a water based moisturiser which does help. This was much cheaper.