Internet-of-drones (IoD) systems require enhanced data transmission security and efficient interference management to accommodate the rapidly growing drone-based and rate-intensive applications. This paper develops a novel resource allocation scheme to jointly manage interference and enhance the physical layer security of cellular-connected IoD networks in the presence of a multi-band eavesdropping drone. Our envisioned cellular-connected IoD network has multiple full-duplex cellular base stations (CBSs), where each CBS reserves an orthogonal cellular radio resource block (RRB) for the aerial communication links. To efficiently utilize the cellular RRBs, each CBS is connected to a cluster of data transmitting drones using uplink non-orthogonal multiple access (NOMA) scheme. In addition, all the CBSs simultaneously transmit artificial noise signals to weaken the eavesdropper links. A joint optimization problem, considering the transmit power allocation and clustering of the legitimate drones, and the jamming power allocation of the CBSs, is formulated to maximize the worst-case average sum-secrecy-rate of the network. The joint optimization problem is decomposed into drone-clustering and power allocation sub-problems to obtain an efficient solution. A multi-agent reinforcement-learning framework is devised to solve the drone-clustering sub-problem. Meanwhile, the transmit and jamming power allocation sub-problem is solved by employing fractional programming, successive convex approximation, and alternating optimization techniques. By iteratively solving these two sub-problems, a convergent resource allocation algorithm, namely, security and interference management with reinforcement-learning and NOMA (SIREN), is proposed. The superiority of SIREN over several benchmark schemes is verified via extensive simulations.