This paper studies the problem of feedback allocation and scheduling for a multichannel downlink cellular network under limited and delayed feedback. We propose two efficient algorithms that select the link states that should be reported to the base station (BS). A novelty here is that these feedback allocation algorithms are performed at the users' side to take advantage of their local channel state information knowledge in order to achieve higher gains. The first algorithm is suitable for a continuous-time contention scheme and requires only one feedback per channel, whereas the second one is adapted for a discrete-time contention scheme and adopts a threshold-based concept. For this second algorithm, we study some implementation aspects related to the feedback period and investigate the tradeoff between knowing at the BS a small number of accurate link states and a larger but outdated number of link states. We show that these algorithms, combined with the Max-Weight scheduling, achieve good stability performance compared with the ideal system.