Physical and psychological symptoms lasting months following an acute COVID-19 infection are now recognized as post-acute sequelae of COVID-19 (PASC). Accurate tools for identifying such patients could enhance screening capabilities for the recruitment for clinical trials, improve the reliability of disease estimates, and allow for more accurate downstream cohort analysis. In this retrospective cohort study, we analyzed the EHR of hospitalized COVID-19 patients across three healthcare systems to develop a pipeline for better identifying patients with persistent PASC symptoms (dyspnea, fatigue, or joint pain) after their SARS-CoV-2 infection. We implemented distributed representation learning powered by the Machine Learning for modeling Health Outcomes (MLHO) to identify novel EHR features that could suggest PASC symptoms outside of typical diagnosis codes. MLHO applies an entropy-based feature selection and boosting algorithms for representation mining. These improved definitions were then used for estimating PASC among hospitalized patients. 30,422 hospitalized patients were diagnosed with COVID-19 across three healthcare systems between March 13, 2020 and February 28, 2021. The mean age of the population was 62.3 years (SD, 21.0 years) and 15,124 (49.7%) were female. We implemented the distributed representation learning technique to augment PASC definitions. These definitions were found to have positive predictive values of 0.73, 0.74, and 0.91 for dyspnea, fatigue, and joint pain, respectively. We estimated that 25 percent (CI 95%: 6-48), 11 percent (CI 95%: 6-15), and 13 percent (CI 95%: 8-17) of hospitalized COVID-19 patients will have dyspnea, fatigue, and joint pain, respectively, 3 months or longer after a COVID-19 diagnosis. We present a validated framework for screening and identifying patients with PASC in the EHR and then use the tool to estimate its prevalence among hospitalized COVID-19 patients.