Speaking as a mom (daughter is 18 and just started college) and as an educator (substitute teacher over 12 yrs mostly in 1st grade)
Your son is going through a huge change. Small school and 1/2 day kinder to a large school and all day 1st grade is stressful.
The K program at our elementary school is an all day program and the K's are around the other students often in order to make adjustments to school. STILL, many of the children feel stress when they start 1st grade. I think there is more pressure to perform due to spelling tests that are now given weekly as well as timed math quizzes which are just to get a guide for where the student stands on those subjects and where we need to target any special concerns for academics.
Socially, it is still a change. The grade level is different, schedule is different, some children have matured a bit and others not, the list goes on and on.
I've had many parents stay in the classroom until all announcements were over and I was starting class. Then, when parents start to leave, some children decide they don't want mom to go and then there is a bit of disruption in the classroom which in turn embarrasses the student in front of his/her peers. In no way am I suggesting you have gone overboard... I'm only stating what I have witnessed. Some schools have rules in place that parents do not walk to the classroom. Our school has not done that because we do want parent involvement but it is encouraged to drop them off at class, say your goodbye and move on.
Of course your son is overwhelmed and it make take a couple of weeks to get into the routine. Please do check with the teachers because most of the time, the students who are stressed about leaving mom and the change are ok during school when they are in groups, etc for class. I know if a teacher is aware of some extra stress on a certain child, we do make extra effort (as a teaching team) to make sure that child gets what he/she needs.
I am sorry I have no magic words for you except to be patient, loving and try not to let him pick up that you are feeling so badly for him. Don't bait him with questions if someone isn't nice, etc.
Make sure he gets good rest, good breakfast and if you feel the need, maybe have a reward system in place for him at the end of the day which adds up to a special treat or something at the end of the week if he has all smiley faces, etc from the teacher in his daily report.
Best wishes!