You need to do optimization of server. You don’t need to upgrade anything on DigitalOcean. You already have SSD storage, which is fastest available.

For static images or images you upload to site manually, compress it. There are many services that can do it for you. I can recommend TinyPNG. I think it’s great service for compressing PNGs and JPGs, in my case, results was great.

Little tinkering on server can help. Setup caching correctly, it can help a lot, as it stores content in clients Browser. How to Implement Browser Caching with Nginx’s header Module on Ubuntu 16.04.

You need to find a way to compress image before uploading, if end user is uploading, and you can’t use some service like TinyPNG to compress image, you need to find way to do it client/server side.
There is GZIP compression, but if you go over How To Add the gzip Module to Nginx on Ubuntu 14.04 you’ll see that GZIP is not giving so much results. You can give it a try and see if it’ll go well for you, but I don’t think so.
Maybe something like J-I-C ~ Javascript Image Compressor (github.com) can help, but I never used it and don’t know is it working on giving results.

You can think about setting up some CDN solution so you can delivery content to users faster. There are many services that can do that for you, free and paid. Usually I recommend CloudFlare, as it’s probably most popular and wide used service for CDN and much more.

You need to try and see does something of these help you. I hope you’ll make it work better. ;)