Upvote:0
I am not certain about American (as I don't fly them), but with other US based carriers, Delta and United, if your layover is more than 12 hours overnight you have to claim and keep your bags, then recheck them the next day. They will not keep the bags for extended periods (they lay the reason as security).
I would call American direct and ask what their policy is. Then you can plan your lodging and such. Your hotel in Miami maybe able to hold the bags for you while you run to South Beach.
Personally I would rather have my bags with me, then laying around on a bag cart at MIA for the night.
Upvote:2
You do not need a real visa as Spanish and British passport holder but you need an ESTA which is basically a simplified electronic visa offered to a number of countries part of the visa waiver program.
For the layover is Miami, you will receive your bags and have to check them back in. Depending on your arrival time, you may be able to do this right away instead of taking them with you, as long as you have completed the check-in for the last leg of your flight.
Just 3 days ago, I did a similar path via Miami on American but to Ecuador instead of Colombia. I was in Colombia 3 weeks before though, it's very similar as long as you go via Miami. Every time, I had to get my bags and check them back in.