Though it wasn't really a mistake to file in Texas, you will have a problem trying to enforce your Texas judgment against a debtor in Florida.
Here is the situation:
Your Texas judgment is only enforcable inside Texas. If the 'ex' has non-exempt (seizable) assets in Texas, those assets can be used to enforce his paying the judgment.
However, if all his assets are in Florida, the Texas judgment can't 'reach' them. You will have to transfer your judgment (called 'domestication') to the Florida court system. This is done by sending an certified, exemplified ORIGINAL of your Texas judgment (you get that from the Texas court) to the appropriate Florida court, with payment of a FL filing fee. The Florida court then records your Texas judgment (and gives it a FL case number) and gives the FL debtor a chance to challenge the validity of the Texas judgment (Not the facts of the case, just the validity). If he doesn't challenge, or fails on his challenge, the FL court will issue a valid FL judgment in your favor and you can use the FL judgment to enforce against his assets in FL.