Chimerism
It can happen, usually due to a reproductive error at the biochemical level, that an organism contains cells from a different genetic line. Sometimes two eggs fuse or one egg develops with two sperm, or (as in this case) two embryoes fuse. In-vitro fertilization makes this condition more probable because of the number of embryoes typically implanted (normally only one will grow to maturity). Generally the immune system learns to recognize both sets of cells as "self" and the extra cells may cause no harm. In other cases (such as this one) the cells work incorrectly or not at all, with consequences ranging for the merely irritating to the life threatening, depending on where the cells are located.

House: (About a high-definition television set that the gang is using to watch a heart monitor) Foreman, I need you to steal one of these for me.
Foreman: (sarcastically) I'll ring up one of the homies.

Mother: You're talking about brain surgery.
House: I'm talking about really cool brain surgery.

"I was afraid your wings would melt"
Wilson refers here to the story of Daedelus and Icarus. In Greek mythology, Daedelus constructed wings of wood, wax and feathers so that he and his son might fly. The experiment worked, but Icarus, caught up in his new ability, flew too close to the sun. The wax melted, the feathers came loose, and the lad plunged to his death. The moral, if you like, is not to overreach yourself. (The Greeks believed the sun was a fire pulled through the sky each day by Apollo. To them, flying into the sky could easily put one in close proximity to it.)