One thing that will really set a DIY racquetball broadcast apart is a scoreboard.
If you are only using a phone or tablet, then I recommend SportCam by RankedIn. This will put a scoreboard that you can customize on the stream and will take the video from your device either to your Facebook account or to your YouTube account. This app can also be controlled by a smartwatch, so you can be on the court playing and still get the benefits of a scoreboard on your recording/broadcast. It is initially free for two weeks and then can be purchased for $40 per year.
There are also more complex apps, that will let you add commercials or floating logos to recognize sponsors, like ScoreCam. I haven’t used ScoreCam so I cannot specifically recommend it, but it might be worth a try if your broadcast needs are growing towards needing to run commercials during timeouts and breaks between games and you have an income stream to pay for the subscription required.
If you are moving beyond a phone or tablet and towards a camera or two, then you can run your camera into a computer (Mac or PC or Linux) and use the free OBS Studio. You can then use numerous scoreboard options, including something as customizable as a spreadsheet cropped and loaded as an overly. This setup process is much more complicated than the phone apps above, but also much more versatile. If you will eventually want to run ads during timeouts or between games, then this is a good software to start getting used to.
Another option if you don’t want to acquire a laptop with a new enough and powerful enough graphics card to perform the encoding and streaming, is to use a tool like an ATEM Mini Pro ($300+) and then use H2R Graphics to coordinate any and all graphic overlays that you may need, including a scoreboard. I used this setup with a Microsoft Surface Pro 3 and was quite happy with it.
If you want the best repeatable broadcast setup, I recommend vMix. The $60 version (Basic HD) will include the tools to build and customize your scoreboard and keep you from running multiple programs during your broadcast. Both the $700 version (4K) and subscription version (Max) will add the option for instant replay, and this is the primary reason I use and recommend vMix. Instant replay takes the broadcast from ho-hum to attention grabbing and professional quickly! There is a free 60 day trial with vMix, so you can easily get it installed before your event and work with all of its tools to ensure your best results before paying for the software. I use the subscription version and cannot recommend this product enough.