M., I absolutely abhor bribery as a means to get children to perform a desired task. It inspires the wrong standard for appropriate conduct (or anything else) and they learn to expect a reward for behaving correctly. I also dislike medications as a 'first line of defense' for problems in children. Although there are times when medication is, absolutely, the best and most appropriate treatment, I would hesitate to jump to that avenue too quickly.
Did your son have issues with going to school last year? Is he at the same school this year? With the same group of classmates? Other than the teacher, is there anything else in the school environment that may have changed? There are so many possibilities of what might have triggered the current reaction in your son. (When my daughter was in first grade, we were driving her dad to work before taking her and her older brother to school one snowy winter morning. We witnessed a multi-car accident on the way. Soon thereafter, she began crying every morning on the way to school. We were concerned that something was wrong at school and she was quick to confirm that diagnosis. At school, however, they were worried that she was coming to school in tears every morning. When they asked her what was wrong, she told them, "Mommy wouldn't give me any breakfast this morning," or, "I was cold and Mommy wouldn't let me bring my sweater." There was always something different until the school decided she was being mistreated and we got an early morning visit from CPS (while I was trying to get out to a college class of my own!))
Then, again, is it possible that there is a new kid in class who bullies your son? Or has the teacher isolated him as her scapegoat. (Don't discount this idea even if the teacher, "seems so nice". Often teachers can seem the perfect ally in raising your child but, when the parents are gone, turn into Nurse Ratchett or the Wicked Witch of the West. It is also not uncommon for teachers to consciously or sub-consciously target one particular child in a class room for punishment or favoritism.)
The point is, there may be no obvious rationale for your son's behavior and it may be years before he can tell you about it. Sometimes, though, you just have to sort of roll with it. Talk to him about what is bothering him. He may tell you, but probably not. Offer suggestions as to what is at the root of his resistance. Regardless of whether or not he tells you what is bothering him, reassure him that you are there for him whenever he has a problem or if he just wants to talk, cuddle, or play. Remind him that, if he has any problems, you will always be there to help him and support him, and defend him.
If you son did not suffer from separation anxiety when he entered first grade, it is unlikely (though not unheard of) that he would suffer the fear now. But regardless of the source of his anxiety, just keep reminding him that you are available if and when he wants to talk about it. Also, don't be too quick to put your son on anxiety meds but, if the therapist determines that would be the best treatment, be sure to get all the information: What exactly will it do? Will it effect his classwork? How long will he have to take it? If you don't like the answers (especially if the doctor indicates your son would be on anxiety medication long-term or lifetime) consider a second opinion.
Good luck.