Hi, Anna! I have been in software engineering for over 20 years. I am self-taught and I have worked alongside people with formal computer science education for most of my career. I have generally found that I have been prepared to address all of the same technical problems that my formally educated peers have addressed.
However, I have found that the past 3-5 years our industry has shifted. I have seen a trend where employers are requiring both formal education AND internships. While you might still be able to self-teach and break into the industry, you will have to work hard to prove that you have the same mathematical and algorithmic "mental muscle memory" as your computer-science-degree-adorned competitors.
If you are going to go the self-taught route, I would advise you to make sure you cover Data Structures and Algorithms. After you have covered that and before you start interviewing, it is a good idea to check out http://www.crackingthecodinginterview.com/
It used to be that just Apple, Amazon and the big shops interviewed like this; but, anymore, even small shops demand similar coding challenges and interview approaches.
I wish you all the best and, if I can offer any clarification, please do not hesitate to ask!