SARS-CoV-2 has undergone repeated and rapid evolution to circumvent host immunity. However, outside of prolonged infections in immunocompromised hosts, within-host positive selection has rarely been detected. The low diversity within-hosts and strong genetic linkage among genomic sites make accurately detecting positive selection difficult. Longitudinal sampling is a powerful method for detecting selection that has seldom been used for SARS-CoV-2. Here we combine longitudinal sampling with replicate sequencing to increase the accuracy of and lower the threshold for variant calling. We sequenced 577 specimens from 105 individuals from a household cohort primarily during the BA.1/BA.2 variant period. There was extremely low diversity and a low rate of divergence. Specimens had 0-12 intrahost single nucleotide variants (iSNV) at >0.5% frequency, and the majority of the iSNV were at frequencies <2%. Within-host dynamics were dominated by genetic drift and purifying selection. Positive selection was rare but highly concentrated in spike. Two individuals with BA.1 infections had S:371F, a lineage defining substitution for BA.2. A Wright Fisher Approximate Bayesian Computational model identified positive selection at 14 loci with 7 in spike, including S:448 and S:339. We also detected significant genetic hitchhiking between synonymous changes and nonsynonymous iSNV under selection. The detectable immune-mediated selection may be caused by the relatively narrow antibody repertoire in individuals during the early Omicron phase of the SARS-CoV-2 pandemic. As both the virus and population immunity evolve, understanding the corresponding shifts in SARS-CoV-2 within-host dynamics will be important.