If you're on a desktop, just download stockfish and then some application to run it in, such as arena. Might need to google up some instructions, but you can get a top rated chess engine to tell you the right move for free. Most times, the free online chess analysis has a lot of limits placed on it. Low search depth, limited hours, etc with paid subscriptions to lift the restrictions. But you can just download a chess engine 100% for free. This stuff is open source.
I mean, I agree with the "low search depth" part, but that's just browser limitations. There's a good few sites that provide the full features of Stockfish in browser for free, such as
You must be registered to see the links
's analysis thing, or the completely free
You must be registered to see the links
. They might not be the fastest, but that's browser limitations. They do provide some good info when trying to learn chess, but if you're just looking for real-time game analysis, then they should be fine. Unless you're looking to play chess more often, then downloading and setting up Stockfish might be a bit much compared to just clicking those links.