To my knowledge, you do not lose the right to own or possess a firearm in Florida when adjudication is withheld. That doesn't mean the same applies in other states or in federal jurisdictions. First off, the feds do not recognize withholds. All sentences are convictions to them. If you are caught on federal land with a firearm, you could be charged with possession of a firearm by a convicted felon. Also, I do not know what Alabama's laws say about this. As well, the rules to get a concealed weapons permit vary from state to state. You need to check with an attorney there about your rights.
Under Florida law you may purchase a firearm, and you may obtain a CCW as long as you have not been under supervision in the last 3 years. The problem is that the federal government does not recognize FL's system of withholding adjudication. Under FL you have never been convicted of a felony and can truthfully state so. If however you are charged under Federal law with possession of a firearm by a convicted felon you will be found guilty. Having a CCW will in most cases protect you from this even becoming an issue or having a full check run just because you are carrying.
One issue you will have is whether the withheld adjudication was reported to the Feds. If so, AL likely will not recognize the withhold. One loophole that is not full proof but may allow you to get around the issue is to apply for a FL CCW as a non resident. AL currently recognizes CCW issued by FL. I am not aware if there is a specific AL provision regarding the use of a recognized out of state license by an AL resident.