I think there are a lot of questionnaires/tools that may address your goals but are not specific to the COVID-19 pandemic. I can only imagine trying to design and further validate such tool in the middle of this pandemic. However, I have seen this study which attempted to do just that: https://www.jpeds.com/article/S0022-3476(20)30336-X/fulltext.
These may also be of interest:
1. Article Factors influencing psychological distress during a disease ...
You can use a scale on Perceived Invincibility which is related to issues of adherence to (Center for Disease Control) health instructions, psychological well-being could also be looked into because of effects of the lockdown. These scales are available online.
Your questions is very specific to psychological effect of covid 19. Personally have not come across such a scale to tap psychological distress due to covid 19. But surely you could look at the common health issues one is likely to face during this time like sleep problems, anxiety, use if social media and coping.
If it is a specific effect(s) of Covid-19, you could always attempt to develop your own using the basis of another questionnaire and adapting that. Alternatively, as Sunil suggested there are others looking at this research, you could ask if they have developed a template or even join up with them on their research. Interested in your outcomes.
I think there are a lot of questionnaires/tools that may address your goals but are not specific to the COVID-19 pandemic. I can only imagine trying to design and further validate such tool in the middle of this pandemic. However, I have seen this study which attempted to do just that: https://www.jpeds.com/article/S0022-3476(20)30336-X/fulltext.