Try not to worry. (Easier said then done I know)
I was referred to the mental health team before I was pregnant, with a non pregnancy related mental health problem.
In my experience it was incredibly hands off.
I actually fell out of the system due to a clerical error and didn't get my appointment and had to chase it up myself. I eventually got CBT, by which point I was pregnant. I had to see a consultant when I was pregnant too, but that was also very non invasive and very hands off. I actually can't remember now if that was for my mental health of because of my weight or both. It was that low key.
Nobody checked up on me, nobody came to see me outside of the normal midwife visits.
After I gave birth I had a bad patch of feeling low and went back to the doctor to get some more medication. The GP just prescribed medication and that was the end of it. Nobody checked up on me, there were no home visits or social workers. Again, it was all really hands off.
In my experience, anxiety disorders are so common that GP's etc don't even blink at them. It wouldn't surprise me if you weren't even the first person that your midwife had to refer that day.
Don't worry that you cried, it's normal to do that. I cried the first time I told my GP how I was feeling. They expect that, they wont' judge you on it.
Also, because medical staff deal with this sort of thing every day they understand that there is a scale of the illness. They will be able to see that your child is not neglected. They don't swoop in and break up families.
Take good care of yourself.