Hello,
My name is Michael Burnley and I am a web developer with 10+ years of experience working in Shopify and Javascript. I am primarily backend and have worked in both a contract and freelance capacity for one of the top Shopify Expert agencies here in the US as well as for small businesses in the US.
Depending on where the products are coming from I don't see any issue with creating a backend script for you to use within a day or two (assuming clear requirements.) Unfortunately, for this budget amount I will not be able to host this for you, but I can help you get it hosted on your own platform/service.
If you have any questions feel free to reach out to me.