Not necessarily, but it improves your chances.
This question comes up a lot in my writing circles, and while I can't fully answer your specific case of writing a university textbook (most of my publishing experience has been with small local magazines and journals), in general for most books the answer to the question of "do I need to hire a proofreader first" is no, but with a big asterisk.
What usually happens is that when you're trying to publish through traditional means, i.e. a large or medium publishing house, you'll have to find and convince a literary agent to take on your case, and you'll sign a contract with that agent to have them work with you on getting your book published through one of their industry contacts. You'll then go through a process of developmental editing alongside that agent before you actually submit your manuscript to a publisher, and they might do multiple rounds of that with you, where they provide copyediting and proofreading for you as part of your contract with them.
Because of this, if you go through the preliminary step of getting an agent first, you don't strictly need an editor before you decide to submit to publishers, since a lot of the editing stages are provided to you as part of your agent's contractual obligations. However, it's still a good idea to hire one if you are really worried about there being a lot of mistakes in your manuscript, since the more mistakes you have, the more "amateur" your manuscript will seem to an agent (and by extension a publisher) and the less likely you are to get their interest. Publishing is incredibly competitive and you want to increase your chances as much as possible, and a highly polished manuscript is the best way to improve your odds. If that means you have to invest in an editor or proofreader first to help you get to the next steps, then that's what you'll have to do, and that's okay. It will reflect poorly on you if you submit a manuscript that is riddled with spelling mistakes and basic grammatical errors, and while it's not at all your fault if you're dyslexic or have other writing/reading difficulties beyond your control, there is definitely a baseline level of professionalism required to get noticed in publishing, and I would highly encourage you to try and hit as high a bar as possible before submitting to anyone for publishing consideration.
If you don't want to shell out money for a proofreader, other, less expensive options would include:
- Having your friends, family and peers look it over and check for spelling/grammar mistakes.
- Ask for a beta reader online or in your writing circles.
- Bring it to a writer's workshop and have a published writer or mentor give feedback.
- Run the manuscript through a spelling/grammar checker software tool, i.e. Microsoft Word's built-in spell checker.
(More information from a good writing blog about this topic.)