Hey @jsangco
I believe your error is being caused by something else, not by being on the free tier. If your deployed app is really resource intensive, then scaling up will be your only option.
Use the Troubleshoot HTTP errors of "502 bad gateway" and "503 service unavailable" in Azure App Service guide to help determine what is causing your issue.
Collect data of your application so you can determine when and where the error is occurring. You can also enable Application Insights through auto instrumentation to help aid with this. Once you determine the when/where, then you can include additional logging statements in your application to capture the root cause(s) of the error in question.