Celine,
I would love to see Eta’s clarification, but I think she had a very strict definition of bilingual: can speak two languages.
Having said that, there is no reason to expect that you can speak both languages with the same level of fluency.
Your educational background prepared you to acquire English as a language in a unique way. Many do not have this kind of opportunity in the US, or even in other places.
Here’s a way to measure bilingualism. Check the ILR () skill levels, and do your own self assessment. There is a link to self assessments at the bottom of the screen.
Typically, you can only translate or interpret what you can understand, so your ability to translate will be limited by your reading and listening skills in the source language.
Your ability to translate or interpret will also be limited by your ability to write or speak in the target language.
By the way, this is a generic you, not a “you” addressed to you specifically!
This is by no means a definitive answer, but it may give us food for thought.

Also, you can become bilingual later in life. I grew up in Germany, lived there for 16 years, went to the US as a foreign exchange student for a year, then went back to Germany for two years and finally moved to the US at the age of 19. I studied English for several hours each week from 5th grade until 13th grade, then went to college in the US (BA in Journalism) and worked as a reporter for a large Nebraska newspaper for several years. I am now 100% bilingual, even though I did not grow up speaking two languages at home. As a matter of fact, if I did have a “dominant” language at this point, it would be English, as that is the language I speak, dream, read, and write for at least 90% of each day. The only way people can tell I am from Germany is by my slight accent – and even with that, people guess Irish more often than German, because they are thrown off by the fluency of my English conversation skills.

I do feel that the concept of true bilingualism is hard to grasp for anyone who is not in fact bilingual. It is difficult to define a strict boundary for bilingualism. But I agree that you can always learn more – whether you are monolingual or multilingual, there are always more words to expand your vocabulary!