I also started to realize how, at times, she had to struggle just like me to keep her head above water.

keep 是动词，意思是"保持、维持"。 her 是代词 she 的所有格形式，意思是"她的"。 head 本义是"头部"，在这里比喻为"生存状态"。 above 是介词，意思是"在...之上"。 water 本义是"水"，在这里比喻为"困境"。 keep one's head above water 是一个习语，字面意思是"保持头部在水面之上"，比喻为"勉强维持生计"或"避免陷入困境"。