I'm a technical founder living in San Francisco. I am good at what I do, but I hate, hate, hate self-promoting. Am I doomed, or am I still able to build cred in my field?
You don't have to be a self-promoter to succeed. If you build a great product that resonates with customers, people will come to you. So the question for you is how confident are you that you can get sufficient traction by yourself or with your current resources? If the answer is "very confident" then don't think any further about brand-building.
To answer your question as you've asked it: The actual brand of a technical entrepreneur is 90% past accomplishments. Where did you go to school, who have you worked with previously and what are the greatest things you've built? These define an engineer's personal brand. The 10% is a function of the respect and general perception held by others you've interacted with professionally.
So, you're by no means doomed to fail. However, if you really hate selling, it's likely that you're going to much more successful in recruiting a co-founder. At some point, your startup is going to rely on selling. Whether you're raising money, recruiting a team, or engaging with customers or industry stakeholders, having an extrovert who loves to interact with people and can translate that message to each different person in the way that they understand and get excited about is going to play a significant role in the success of your business.
Happy to talk to you about what you're doing and where you're at.
You wouldn't be asking this question if you weren't conscious of losing out to more "extroverted" brands / personas.
Without knowing the field, the business, or the details, any advice I (or others) might give may miss the mark.
You are who you are. So concentrate on changing something else.
Assuming you offer a great service or product, then your problem isn't satisfying customers; it's making the right first impression and getting them in the door.
First impressions derive from such things as (1) brand name / domain, (2) graphic design, (3) written content. Obviously that's no complete list. But maybe you can identify one of those for making improvements.