ISA Browns and Golden Comets are two kinds of Red Sexlinks. That same basic kind of chicken gets sold under many different names.
Yes, she probably did lay those eggs. Her comb and wattles look big enough and red enough for her to be laying.
So either she matured unusually early (maybe because the days were getting longer at this time of year?), or she was older than you thought when you purchased her. Some chicks naturally do get their feathers faster or slower than others, so if she was a slow-feathering chick she might have looked young while actually being a few weeks older.