I know this probably wont get best answer but. worth giving it a shot.Keep them moisturized with a clean and possibly new lip balm.Something your using on your lips is irritating them to have them flare as so. or maybe something your using now which is causing the reaction. stop using newly used products and wait till it clears up. then later when your clear, test them to see which one it is. good luck on that.In the meantime I use spectro eczema intense re-hydration cream ( works amazingly) and maybe try some Burt’s beez lip balm ( both very moisturizing and hypoallergenic). Try using an ice pack or cold substance and place it on your lips ( not directly, with a cloth because you don’t want frost bite from the cold). It should help the swelling go down from the eczema.If not, go to your doctor and or dermatologist and he.she can help 
Good luck and get healed! 
Do NOT use any lip balms that are minty. I went to the dermatologist, and he said that it only makes the condition worse – it feels better for a little, but it’s really hurting your lips. So use vaseline, or vaseline lip therapy is good too.
I would not give the child primrose oil. That is generally used for women. Put into thirds. .that should do it for him.
I have the same thing. My derm prescribed Polytar shampoo and Elomet lotion (or Beprogel if you can’t find Elomet).
just because it never showed up you are actually allergic to the food , dosent mean it still wont aggravate or bring out eczema. well my sister has the same problem too and the drugs she uses are afective only for a short period of time.