uhhhh this is a bit awkward coming back after thinking I have done it all but it turns out that my fan is producing some sort of electric noise that is messing up the lm35 sensors readings. Like, before i powered on the fan it could read the temperature well at a stable 21-22 degrees celsius, but after i powered it on with a 12V DC adapter to the arduino uno the readings become very unstable.
Actually, my lm35 sensor was also unstable for a bit until I added in a 10 microfarad ceramic capacitor (i added in another in parallel for extra measure), so I thought I could possibly do the same with the fans wires but im unsure how to go about it.
The circuit is pretty much the same as the last picture except a capacitor across the LM35 as well as the capacitor over the railings being removed. Sorry for rushing to conclusions earlier, I was so tired over this that I didnt fully check it lol. Also to answer your question i do not have one though i could go out and buy one later, and the power supply is connected to the arduino unos barrel jack.