If there is not much traffic initially, can you consider just hosting that at home. You can use dynamic dns to point a domain back to your home ip address.

Once you start receive real user traffic, you can consider move to public cloud. If you can build everything into docker containers and user serverless database option, the price won’t be that bad until you hit critical mass.

Have you try other online services (no insurance need) like GoodRX care? I don’t see you need 16 or older for UTI in their options.