This sounds SO much like my 9-yo cousin.
She WAS partially breastfed (but supplemented w/formula from almost the beginning and on table foods at 3 months - both b/c "she was hungry all the time"). Her first "finger food" was m & ms. Her typical "breakfast" is 4 slices of heavily buttered white toast and a bottle of diet Pepsi. She eats mostly fried and heavily processed foods, but she loveslovesloves milk. She seems to CONSTANTLY have cold symptoms, and she's been overweight since she was a toddler.
Her older brother developed a suspiciously sudden (and supposedly lethal) allergy to eggs, at the age of 15.
Of course they are both vaccinated according to every and all recommendation. I reminded my aunt that her son should not get certain vaxes b/c of the egg allergy...