What are these white lights/dots I'm seeing in the sky?

I believe migratory birds will sometimes fly to what seems like an absurdly high altitude over land, before setting out across water (probably both to exploit thermals, and just for general prudence.

Bird strikes on aircraft are common at and above 5000 feet altitude, so birds definitely go that high - and a gull would be little more than a speck at that distance, to the naked eye.

Probably balloons. If they are the larger, registered variety, they can be tracked at https://www.flightradar24.com. This particular link is a look at the Gulf of Mexico. Just now, there are at least five in one area, three of which are floating surprisingly close to one another. You can do a search on that site for “HBAL”, and it’ll list quite a few balloons to choose from.