After leaving a team, it may take some time for the system to recognize that you've left. This may result in a delay before you're able to join another team. Also, please note you won't be able to join a team if you have been previously kicked out from it. If this is the case, you will need to be invited to join the team to be able to be part of it again.
If you're trying to join a "private" team, please remember that you can only send one invite request to a team at a time. You will not be able to send another request if you're still in a team, or if your previous request still appears in the chat window of the team it was sent to, even if this request has been rejected. You can join a team immediately if you get a direct invitation from the team captain / vice captain.
Just hang in there for a bit longer - you'll be able to join another team before you know it.