You can find an ongoing compendium of work by the COVID-19 Mental Health Measurement Working Group here.
Holingue, C., Badillo-Goicoechea, E., Riehm, K.E., Veldhuis, C., Thrul, J., Johnson, R.M., Fallin, D.M., Kreuter, F., Stuart, E.A., and Kalb, L.G. (2020). Mental Distress during the COVID-19 Pandemic among US Adults without a Pre-existing Mental Health Condition: Findings from American Trend Panel Survey. Forthcoming in Preventive Medicine. Available online 3 August 2020. Article Link
Riehm, K.E.., Holingue, C., Kalb, L.G., Bennett, D., Kapteyn, A., Jiang, Q., Veldhuis,C., Johnson, R.M., Fallin, M.D., Kreuter, F., Stuart, E.A., and Thrul, J. (2020). Associations Between Media Exposure and Mental Distress Among U.S. Adults at the Beginning of the COVID-19 Pandemic American Journal of Preventive Medicine. Article Link
Kreuter, F., Barkay, N., Bilinski, A., Bradford, A., Chiu, S., Eliat, R., Fan, J., Galili, T., Haimovich, D., Kim, B., LaRocca, S., Li, Y., Morris, K., Presser, S., Sarig, T., Salomon, J.A., Stewart, K., Stuart, E.A., and Tibshirani, R. (2020). Partnering with a global platform to inform research and public policy making. Survey Research Methods. Journal of the European Survey Research Association 14(2). Survey Research Methods during the COVID-19 crisis : 159-163.
McGinty, E.E., Presskreischer, R., Han, H., and Barry, C.L. (2020). Psychological distress and loneliness reported by US adults in 2018 and April 2020. Journal of the American Medical Association. Published online June 3, 2020.