I'd say it was "Frederick" if you choose to accept what you've been told. Birth certificates, which are usually considered "Primary" sources, are 'merely' government records, and don't neccessarily reflect everything that was in your parents' minds when they named you.
There are many examples of folks who were not yet named when their birth certificate was issued and were noted as "Infant Smith" or "Baby Smith" or "Female Smith". This does not happen in the modern age, but I doubt anyone would argue that those people's "true" names are "Infant, Baby, or Female".
While it is not that unusual to have a middle initial without middle name, there are examples where one was forced on a person. My paternal grandfather was told when he joined the Army that he had to have a middle name. When he said he only had a middle initial, they chose one for him beginning with that initial and it was used for the duration of his military service.
When he retired, he reverted to just using the initial on all subsequent records and paperwork for the duration of his life. His Death certificate and Grave Marker both use only his initial - so he had the last word.
If you are concerned about what your legal middle name is, I suppose that would be better answered by a lawyer - and I'm not a legal expert. I don't know what the conventions are where you live, but it's likely you may choose to use or not use "Frederick" without having to worry about it. - Mike