My child’s account.

No, my account is not a child's on a family account. It says that I am an adult on my family's account, not a child.

It is my understanding that the child accounts I have setup for my kids will transfer to adult accounts when they turn 18. This means their achievements and games purchased with the child account will now be a normal adult account.

For example, I have XXX24 setup as the parent account with child accounts YYY24 and YYY25. When YYY24 turns 18 the account is now removed from being a child account attached to XXX24 and is now a standard account keeping the gamertag YYY24 and all achievements
and digital games purchased with that account. Someday when my kid "YYY24" has their own kids it will be a parent account with new child accounts under it.

The only difference between a Parent Account and a Child Account is that one resides under the other. With the right settings, a Child Account can have the same unrestricted access as the Parent Account. My oldest child does not have any restrictions on
their account so it really is similar to a standard account.

There is no adult account for my child account so I cant change my child account setting. I want to purchase something but cant since i cant find my adult account. When i press on family, it only comes up with my child account.

Everything is bound to the account/gamertag. If you have a child then they should be on a child account which does let you set restrictions.

Manage account: Child accounts

Evidently having a child account there can be restrictions on the games, here is a link for how to manage the child account https://support.xbox.com/browse/my-account/manage-account/Child accounts