We address the client-selection problem in federated learning over wireless networks under data heterogeneity. Existing client-selection methods often rely on server-side knowledge of client-specific information, thus compromising privacy. To overcome this issue, we propose a client self-selection strategy based solely on the comparison between locally computed training losses and a centrally updated selection threshold. Furthermore, to support robust aggregation of clients' updates over wireless channels, we integrate this client self-selection strategy into the recently proposed type-based unsourced multiple-access framework over distributed multiple-input multiple-output (D-MIMO) networks. The resulting scheme is completely unsourced: the server does not need to know the identity of the clients. Moreover, no channel state information is required, neither at the clients nor at the server side. Simulation results conducted over a D-MIMO wireless network show that the proposed self-selection strategy matches the performance of a comparable state-of-the-art server-side selection method and consistently outperforms random client selection.