We consider a multi-carrier and densely deployed small cell network, where small cells are powered by renewable energy source and operate in a full-duplex mode. We formulate an energy and traffic aware resource allocation optimization problem, where a joint design of the beamformers, power and sub-carrier allocation, and users scheduling is proposed. The problem minimizes the sum data buffer lengths of each user in the network by using the harvested energy. A practical uplink user rate-dependent decoding energy consumption is included in the total energy consumption at the small cell base stations. Hence, harvested energy is shared with both downlink and uplink users. Owing to the non-convexity of the problem, a faster convergence sub-optimal algorithm based on successive parametric convex approximation framework is proposed. The algorithm is implemented in a distributed fashion, by using the alternating direction method of multipliers, which offers not only the limited information exchange between the base stations, but also fast convergence. Numerical results advocate the redesigning of the resource allocation strategy when the energy at the base station is shared among the downlink and uplink transmissions.