For starters, I recommend she get an allergen test from a specialist to see if she has base metal allergies from a doctor since she got an infection from her earrings.
If this is confirmed, get quality gold or sterling hoop earrings just large enough to go around the ear, and have her rotate them several times daily for the first two months to make sure her ears do not try to grow over them(fresh piercings are seen by the body as an irritant, and that is the bodies natural defense, or how my family physician described it to me).
She also has to keep her face, hair, and ears clean and free from sweat, dirt, and oils to prevent clogged pores there, which is...not a pleasant sensation let me tell you, especially when I had to get it drained by my Mother. I kept my hair, face, and ears very clean after that, and wiped them down with witch hazel just before going to bed.
I was six when I got mine pierced. After my Mother did them, we went to the family Physician, who not only inspected them, he explained everything on the care of the skin after a piercing(to explain, back when I had it done, many Mother's did it themselves, and it was only eleven years after I got mine pierced that we saw the first piercing shoppe in our local mall appear...just in time for my sister to have it done there).
If the hole is closed, you will have to wait and re-pierce them so you don't get an internal double hole(this happened to my Mother).
I have base metal allergies, and actually had to resort to making my own hooks (I got a wire bender designed to make earring wires, and made lock-back hooks so they'd not come out at night or get lost from falling out), and bought anodized Niobium(soft enough to bend, rigid enough for jewelry, and comes in many colours, or base plain which looks silver) so that everyone that gives me cute beaded earrings can actually see me wear them(some don't realise I have allergies because I make my own earring wires for long dangling earrings), as I just transfer the beads to the new wires and hooks I make.
I cannot use surgical stainless or hypoallergenic earrings, as the alloy metals give me a reaction(this means either a kids plastic watch, or no watch as well). I cannot use plated earrings either, as the plating wears off--fast. Even my glasses frames are titanium as my allergies are so severe.
Luck to you Grandmama!