Sounds just like my kiddo. K (my daughter) has severe anxiety - it started in kindergarten with the same types of worries but she also has excessive fears of bugs, grass, dogs (at the time) etc.
For her we did a couple things - every day instead of letting her focus in the hard stuff we had her tell us one or two things that made her laugh or that she learned and then expanded on that. We also talked to her teacher to find a peer group that we then reached out to outside of school walls so she could get to know them.
Lastly, one might a week, we let her pick her dinner choice to encourage her to eat. It became part of a routine she loved.
What we found was her anxiety was driven from needing a plan. She needed to know exactly what was going to happen when so we worked with her teacher to lay out the scheduled. Once she understood and knew what was going to happen, she got a bit better. We still have to do that to this day and she is in 5th grade. When she is encountered with a day or an hour without a plan she gets anxious all over again. In kindergarten we kept it simple - wake up at this time, eat at this time, see your teacher at this time, see mom at this time - and so on. She would watch the clock (gave her the big numbers before she could really tell time - when the big hand is on the 1 for example). It really helped her out tremendously.
Now that she is older we sit down at the start of every school quarter and draw out her schedule - she has it on a white board in her room for at home stuff and taped to her desk for school stuff.
It seems like it might be a little extreme, but when we started it - and saw what happened when we stopped it (nail biting, loss of appetite etc.) - we realized for her, it really did help.