Does my child need to see a child psychiatrist or psychologist?

My 3-year old kid recently has a severe phobia attending school ever since she got promoted to nursery with a new classroom and new teachers recently in Dec (1 month). For the first 2 weeks, everything seemed quite fine except she doesn’t nap in the afternoon anymore but she napped daily when she was in her previous pre-nursery class (attended 10 months). Lately she has been crying very badly and repeating like a cassette recorder for 2 entire days & daily saying she didn’t want to go school anymore and the new teachers were very fierce with her. She mentioned she’s afraid of seeing them. She also said the teacher beat her backside several times when we asked her why she doesn’t enjoy schooling anymore like she really used to be? We also don’t know how true it is but hearing she has been repeating the same story over & over again made us somehow trusted in her. We also spoke to the principal regarding her recent condition but not much info was revealed as the cctv footages can’t be viewed by us. And there’s one recent incident where she fell on her boy classmate when playing in class causing the boy to lose balance and hit his back of the head accidentally which may have startled or traumatised her. Till date, everyday she will keep telling me any time of the day she doesn’t want to attend school and every night before sleeping she will cry & tell me many times she doesn’t want to go school again and again. We can’t even mention the word “school” to her, if we did or when she is reminded of school, she will start to feel nauseous then followed by vomiting episodes. In the middle of each night, she will wake up crying from her terrible nightmares saying she doesn’t want to go school again. When i am taking her to school or on the way she will start to cry and want to vomit. The moment she reached the school, she will feel nauseous and vomit a lot in front of her class or when she entered her classroom after the compulsory morning checks. She will cry really loudly and also have a lot of resistance going into the classroom, she even hugged me so tightly like I am never coming back for her. She will screamed, asked for me “mummy” and teachers have to pull her away from my arms. It has been on-going (vomit issue) for almost 2 weeks plus till now. Her morning milk intake (breakfast) at home used to be 240ml and now it only became 100ml. When she vomited out all her milk in the school in the morning, there’s nothing left in her stomach. Her whole appetite also changed very drastically. She no longer drinks or eats well (her lunch), 1st milk (before nap time), snacks (tea break) and 2nd milk (before going home). Teachers have been reporting to me she barely eat anything for her meals in school daily and even totally refused to drink 2 milk as she’s afraid she may vomit after taking the milk. At home before this phobia happened, she enjoys drinking milk and eating well for her solid food (meals). She used to drink 800 to 1000ml of milk daily including the ones she drank at school & at home and ate 1 solid food meal after school for dinner. Now she has changed entirely and her milk intake per day is only 200ml, which is worrying us so much as she doesn’t drink or eat well, yet keep vomiting all the time day and night whenever she thinks of going to school and seeing her new teachers the next day. All her eczema also broke out badly which I assumed it’s linked to her stress and anxiety. Many months before all these happened, she is looking very forward to her birthday celebration in school as it’s her first celebration after she enrolled into schooling. We planned far ahead & ordered her fave character cake, bought all the necessary decor for the big day but now whenever we talked about the word “cake”, she will cry and tell us she doesn’t want birthday cake anymore as she’s very clear and knows in order to cut cake for her birthday, she will have to attend school. We felt so sad as she used to be telling me how excited she was knowing she’s going to have her first birthday celebration in school with her classmates. She has been affected that she no longer look forward for her big day now too. We can’t figure out what’s wrong and what really happened to her suddenly? She has slimmed down a bit since she can’t eat or sleep well. And I am heartbroken to be honest as I don’t know how to aid or help my poor kid who is in desperate need. She can’t tell us much exactly what’s going on for her as she’s only coming to 3-years old but we really feel her SOS outcries. I don’t know how much longer she can still bear but as a parent, I can’t bear this see her being in this state any further. Please can anyone advise if we should bring her to see a child specialist (psychiatrist or psychologist) for her case. She has been mentally & emotionally tortured at such young age which we are very concerned if she will be affected for her physical development. Does anyone happen to have the contacts of a Child Psychiatrist or Psychologist? If yes please PM too. Thank you and hope to hear more useful replies & advices from you all asap!