Ultrasound (US) is a non-invasive yet effective medical diagnostic imaging technique for the COVID-19 global pandemic. However, due to complex feature behaviors and expensive annotations of US images, it is difficult to apply Artificial Intelligence (AI) assisting approaches for lung's multi-symptom (multi-label) classification. To overcome these difficulties, we propose a novel semi-supervised Two-Stream Active Learning (TSAL) method to model complicated features and reduce labeling costs in an iterative procedure. The core component of TSAL is the multi-label learning mechanism, in which label correlations information is used to design multi-label margin (MLM) strategy and confidence validation for automatically selecting informative samples and confident labels. On this basis, a multi-symptom multi-label (MSML) classification network is proposed to learn discriminative features of lung symptoms, and a human-machine interaction is exploited to confirm the final annotations that are used to fine-tune MSML with progressively labeled data. Moreover, a novel lung US dataset named COVID19-LUSMS is built, currently containing 71 clinical patients with 6,836 images sampled from 678 videos. Experimental evaluations show that TSAL using only 20% data can achieve superior performance to the baseline and the state-of-the-art. Qualitatively, visualization of both attention map and sample distribution confirms the good consistency with the clinic knowledge.