Can you be charged for invoking your right to remain silent?

I was stopped by a bicycle officer in my neighborhood while walking home. There have been a lot of burglaries in my area. This was used as the basis for the stop, though the officer is aware I do live in the area, due to other foot stops. She wanted to know what I was carrying in my bag, which happened to be books, which I opened and showed her. She can began questioning me about where I been, where I was coming from, and begin asking further questions, like what did I eat for lunch when I answered I was coming from Subway, how was the sandwich prepared, what was the name of the person who handled my order, did I have a receipt. Then she began questioning me about the books I had, why was I reading this book, what was this book about, etc. I started to get fed up, so I asked if I was being arrested, which she replied no, then I said I did not wish to answer any more questions, and was invoking my right to remain silent. At this point two other officers arrived on the scene in cruisers, at which point I was placed in cuffs and told I was being charged with resisting an officer without violence. It was later explained to me on the way down to the station that by law I have to answer any and all questions when stopped, and refusal to do so constituted resistance. When I said I had invoked my 5th Amendment Right to remain silent, I was told that first off, unless I've been arrested and/or mirandized, I do not have the right to remain silent when being interviewed by a law enforcement officer, and must answer all questions truthfully during a routine stop, or it is resisting. Then the officer went on to tell me that I was lucky that was all I was being charged with because she could have charged me with assault on an officer if they wanted to push it. All they have to do is show reasonable fear for their safety, and when someone is uncooperative and resists, that creates reasonable fear for their safety, and it has successfully been argued in court.