2 month old baby cannot stay asleep unless held

Hi mummies, I have a 2 month old baby and she cannot stay asleep unless held. I put her to sleep in my arms but the moment I put her down, she becomes wide awake and starts to cry and scream until her face and eyes gets red. I have tried to put the baby down while sleepy but awake, pat to calm her when she cries/make fuss, repeat the steps until baby falls asleep. However the more I try the more cranky the baby gets. How can I make her sleep in the designated sleeping place? I’ve been holding her throughout the day (she did not like the carrier) she is a short sleeper during day time (for some reasons, baby can lay flat and sleep at night for 4-5h), so I am very exhausted….:( I Would appreciate any advice from you! Thank you.