It appears that your pullet is having some problems with her reproductive tract. More than one yolk was probably released from the ovary at a time, causing both to travel down the oviduct and have some albumen (white) added to them. If a shell had been added, this might have resulted in a double-yolked egg, two eggs stuck together, or two eggs laid soon after another. For some reason, though, your pullet's Uterus/shell gland (where the shell is added) isn't functioning properly, and didn't add much shell to either of the eggs.
This problem will likely resolve itself in time. It is not uncommon for pullets to have a few "odd" eggs due to their reproductive system maturing. I would, though, be sure to purchase some oyster shell, or at least crush some egg shells and give it to your birds. This will ensure that they have enough calcium in their diet. Also, are you feeding them layer feed at this point? When pullets begin laying, their nutritional needs change, with them requiring less protein, and more calcium/phosphorus. Only layer feed can provide this.
Good luck, I hope your pullet starts laying some beautiful eggs soon!