You can absolutely have symptoms outside of the home that you don't see at home. My son was diagnosed with sensory integration disorder - which is what a lot of autistic/asperger kids also have. My son was GREAT at home - where the routine was set and he was comfortable. But, I could see how things outside of the house bothered him. He didn't like crowds or noise or "strange things" (which, there were LOTS of strange things to him). One day, my babysitter called me and said he was having a serious meltdown (which I had never seen him have ever) and so that is the point where I got him evaluated and learned that he did have a disorder. So, yes, you can absolutely have symptoms and issues outside of the home.
You need to 100% take advantage of everything that they offer you. My son was very young when he got his diagnosis, so we did not get any help through the schools. We did all of our therapy sessions through private care outside of school. But, the therapies made a HUGE difference for us and so now he is essentially "cured" and does not need help. THAT will not be the case for you if your son does have autism or asperger's. I'm not trying to say there is a "cure" for that, but for sensory integration disorder, my son was tremendously helped.
You also might want to read "House Rules" by Jodi Picoult. It's a fiction story, but it REALLY opened my eyes to an asperger's child's life and what goes on at home vs. out in the world.
The biggest piece of advice I can give you is to let you know that YOU are your child's biggest advocate and YOU will have to step up and reach out and ask/demand for the help that your child needs/deserves. No one else will care as much as you do.
Even though I had no big issues with my child at home, I knew that something was "off" with him from the time he was 5 months old. It was finally the melt down at the babysitters where we got our third evaluation and a professional finally agreed that something was "off" with him and get got help (he was 2 when he entered therapy).
Oh, and just to add an example, my son got his diagnosis and also entered daycare literally the same week (age 2). Prior to that, he was in home care with very few kids. Well, my son HATED sand. Not really a problem in home care - not much sand around. Our new daycare's playground was completely sand. So, he stood there and cried the whole time they were out on the playground. He finally got over that (after weeks) and would go out on the playground. Then, after a year, they transitioned to a new/bigger playground. Well, he just stood there and cried and cried (for three days before the teacher told me about it). One morning, I took him out to the playground and we went over each peice of equipment. I talked him through each piece and showed him how to play on it (without other screaming kids around and he was with me - someone he was comfortable with). After that, he was once again fine with the playground.
Good luck!!!
L.