Emotional parent through routine blood work for 1 year old

Anyone have tips on how to cope with their baby getting blood work or routine vaccines? I absolutely lose it each time my daughter has to get vaccines. My daughter screams and I just can’t bare the thought that she’s in pain and I start to break down in tears. Yesterday was my daughter one year check up and she needed blood work done from a vein on her arm and my daughter sat calmly while the lady put the rubber band around her arm and started preparing the needle. I literally lost it the second she put the needle in and the lady kept losing the vein so she was moving the needle and my daughter screamed so much she started losing her voice and was crying hysterically. I couldn’t keep my composure I literally cried the whole way home while my daughter had already forgotten about the pain. Any tips? 😭