If you simply can't wait until the gameweek is complete and the official FPL site has updated the manager rankings, here are 3 websites that let you track your projected overall FPL rank in near real time. Bear in mind that bonus points allocations can sometimes change well after matches are complete. Also consider that if you're obsessing over your live rank, this is a good indicator that you might be taking the game a bit too seriously. Think about your mental health. If live rank drops etc. are significantly affecting your mood, it might be time to step back a little.
This site will show you your new rank pre-autosubs and post-autosubs, along with a comparison of your score vs the top 10k managers. Ranks are claimed to be >99% exact, and the tool will remember your team ID so you don't have to.
One of many useful tools on this site is their Live FPL Rank & Points tool, which lets you know how many points you have scored from your starting 11, bonus points, and auto-substitutions. I have found the figures to be pretty accurate. Like LiveFPL, it can track any team and will show you green or red arrows depending whether your rank is up or down.
Amongst lots of other useful data about your FPL team and selected mini-league, there is a display of your live overall rank and overall gameweek rank.
Follow your Overall Rank live, and get your FPL management skill rated by their algorithm.
Live gameweek expected and realized points based on match results and forecasts. This site is not simply a live rank predictor; it gives you live graphs of your gameweek points in comparison to expected points and average points. See at exactly which point it all went right or wrong, and how much your team over or under-performed.
Besides FPL discussion, community and stats, the Playmaker app now has a live rank feature.