Does my child have a behaviour problem or?…?
I think she may have a social or emotional problem. Take her to your GP and explain that she is having these issues and get a referral to a behavioural specialist. It may be as simple as needing to retrain her on how to behave socially, or she may have emotional issue that may need counselling. Something may have happened to her that you are not aware of, or she may simply be socially and emotionally immature for her age (not through anything that you may or may not have done, some kids just take longer to develop the skills). You can try talking to her about how to better interact with kids and explain that they may not always want to play with her, or play her games. Ask what has happened when she reacts (with patience) but don’t respond to the sulking or tantrums. Talk quietly and after you have addressed the issue – what is wrong, how can you react better, what can you do to join in – allow her to make the choice whether to join in or not.