You really should visit with an attorney concerning your son's living arrangements. One small change in your fact pattern could change the answer to your direct question. Even if you did not break any laws picking your son up in Florida, your actions could work against you should the father or a third party seek custody of our son from you later in family court.
At age 16 your son may have some say in his living arrangements. Whether or not Dad is on the birth certificate could affect how you proceed. If you need to go to court for help regarding parentage, custody or child support, there may be limitations or options as to which state or states have jurisdiction. There could be claims for child support arrears.
If funds are an issue, contact your local bar association for a low-cost consultation with an attorney. You really need to speak with an attorney before going to Florida to pick up your son.
If we do not have a written attorney-client agreement: I am not your lawyer; you are not my client; this is not legal advice.
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