If I uninstall LR that I had as a trial in order to reinstall a paid version will I lose the photos already uploaded?
Your photos and catalog-of-adjustments will remain intact because they are stored in a separate location than the program, itself, which you’ll be replacing.
A reinstall shouldn’t be necessary unless your trial is CC LR and you paid for a serial-number LR or vice-versa.
For the serial-number LR it’s best to download the very latest version since if you don’t it’ll ask you do update, again, anyway. The latest LR 5.7.1 version is here: