Check to see if the maker of your tablet provides complementary repair services. It might be dead as a doornail or require several hundred dollars to repair, but sometimes you can get things fixed at a reasonable price if you think to ask.
There are keyboards for smartphones which may be feasible for you. I don't know anything about them though, so you'll have to do some research.
Most libraries provide computer services for members. Exact services will vary, but my local library allows you to reserve a computer with a word processor for an hour at a time.
You may be able to find a used tablet for an affordable price. If you're willing to sacrifice on quality and size, the bottom end of the tablet market drops pretty low.
Text to speech technology has progressed pretty far. It's still going to require more editing afterwards (and it isn't great for public spaces), but it might work for you. Even if you can't get a decent text-to-speech app on your phone, you can just record your words and then convert them on your computer or a web service later.
If all else fails, then the only way to get more comfortable at writing in a new form is to practice. Typing on a phone is more prone to errors than using a keyboard so don't worry about getting everything correct the first time, but save your editing pass for when you can get to a real computer.