After swimming out to the sea to spot his mother, why does Jerry feel "relieved at being sure she was there, but all at once very lonely"?

Jerry is not used to being away from his mother. He's only just eleven years of age, and so he has not had a lot of independence or freedom to be on his own yet. He was even somewhat reluctant, as a result of his guilt, to leave her to go to the safe beach on her own, where he used to play when he was a child; however, he can't resist the pull of the wild bay and so chooses to go there when his mother gives her permission for him to do so. Once he is there, he is sort of exhilarated by his independence, but he also, on some level, recognizes that there are drawbacks to freedom as well. He still looks to her for a sense of security—there is some comfort in knowing that his mother is not far away—but the price of his freedom from her is that he is now all by himself, and that is a new and not totally welcome feeling. In the sense that this story is a bildungsroman, or coming-of-age story, Jerry's conflicted feelings regarding his independence convey the idea that growing up is necessary, and it is sometimes fun and exciting, but it can also be very painful and lonely.