I think you have a Free Image Sharing website. You allow users to upload images and share on internet.
You may consider a cheap VPS with nginx.
Nginx servers static files faster.
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What is the maximum limit (MB) you allow to upload image size . I would recommend you for a Dedicated or a VPS for such services. Most of hosting company don't allow copyright material on server. Any complaint could cause a suspension of services. This is comman with most hosting companies.
It is image sharing site where basically anybody can upload any picture on it. But there's no other users except myself uploading pictures from my other sites.
The traffic is too low (less than 100 a day) to consider vps.
Then find a shared host who doesn't offer unlimited space (our silly hundreds of GB), and discuss it with them before you start. I imagine many won't let your have arbitrary upload does because of the high probability that someone will upload copyright pictures and attract DMCA claims, or abusive images and attract DDOS. But they may let you host an upload script for your own private use. (Mind you, in your shoes I'd make sure nobody else is even capable of uploading images, otherwise you have to police it.)