Hey Michelle,
HERE, you will find my guide for stroller cleaning and maintenance, I think it may be helpful for you to read it. The thing I think should help here (if there's not some internal misalignment and that you won't be able to repair, but that's less probable) is to clean your wheels - check for dirt, hair and so on, and then lubricating them as well as that suspension part with e.g. the WD-40. Often squeaking comes in when there's no oiling anymore.
The plastic parts can be oiled too, with a silicone spray - however, be sure not to get that silicone spray on your wheel foam, as that can make that part of the stroller squeak. At least, sometimes that happens.