I joined a squad that was part of a platoon, but noticed that I preferred to join another squad within the same platoon. Is it possible to make that switch?
Yes if you go to your social bar (the one with 2 people shown) you can actually switch by the plus sign next the the squad you would like to join. I would suggest tho u stay in a squad of about 5 people.
If you are a leader of the unit, you can reassign people to squads, including (I think) yourself.
If you're not a leader, you can use chat or voice to ask the leader to transfer you to the other squad.
If you're not a leader and you want to do it yourself, there is no direct UI for it as Young Guilo wrote in April 2013. However, what you can do is make sure there is an open slot in the squad you want to join, note which squad it is you want to join, then leave the platoon, and join the other squad using the list of all squads, which will list each available squad. This won't work if the platoon is set not to allow people to join, or if the squad becomes full before you manage to join it.