I would say she is cremello; her coat color is golden enough she could be palomino, except she has so much pink skin around her eyes and nose. Palominos are often pink in these areas when they are newborn, but the pink soon turns to black. This doesn't look like a newborn foal, so I'm thinking the pink will stay. That means cremello, assuming her eyes are blue? I don't see this as being perlino, but it could be--you'll have a better idea as she sheds out, and of course you might tell more from close inspection than we can from photos.
No, your filly cannot have triple cream genes. Genes come only in pairs! Your filly will have gotten one cream gene from her sire, and one from her dam. The sire has 2 cream genes, but cannot pass both of those on to his foal.