Would you be able to think of any examples and potential solutions for the 2 things she shared? 3 months is too short for a person to prove themselves or determine whether they are capable to do a job or not.
"Do things too slow" There seems to be a mismatch of expectations. Did she share particular examples or context of which you weren't able to meet the deadlines? A friend of mine was expected to reply a client within 15 mins when he was STILL in another meeting with another client. This kind of expectation is purely ridiculous and toxic. If you were clearly given a deadline, did you preempt your boss that you weren't able to meet the deadline a few days before and explain to her why? Was she expecting you to give her instant replies? Perhaps you can think of active steps on managing her expectations so that both of you can come to a consensus that you are delivering your work on time.
"Make too many mistakes" How many mistakes are "too many"? Are they mediocre ones like a typo error or major ones where it affected multiple departments or people? How do you respond to these mistakes and make sure they don't happen again or at less frequency? I think it's normal to make mistakes as we ALL do, but it can be frustrating if she always has to pick up after you. Do you try to double or triple check your work and do you keep making the same mistakes?
As for your self-doubt, I think there are many industries you can potentially explore. I took on many different types of internships, roles and jobs before discovering what I hate, dislike, like, and love. Your identity is not solely tied to a single profession. People switch careers and change jobs. It's never too late for you. Some scientists only invented stuffs when they're in their 80s.
Instead of letting this affect you negatively, let this be a journey of self-discovery in trying to find what you're great at.
I wish you all the best!!