I have a Raspberry Pi 2 Model B, and I plugged in the charger - it was fine. I plugged in the HDMI - still fine. I plugged in the micro SD card (64GB) and the Pi immediately got super hot and when I touched it, it burned my hand. I retried by plugging things in in a different order, and the problem was proven to occur when the micro SD card was in. I even tried different chargers, nothing different happened. Should I get a new SD card, do I need a new PI?
You may need a new SD card. In the worst case, prepare yourself to get a new Pi.
Immediate heat on any component other than a stove or a toaster is not a good sign at all especially in electronics. In a circuit, it usually denotes something is causing a short circuit. In an IC component (like your SD card or the Pi's CPU), it's usually a sign of physical damage to a component, even if it's not visible.
If your micro SD card still works, set it aside and get another micro SD you're okay with breaking (no important data and such). If the Pi still heats up, it's a good idea to replace it (no, you can't fix it).
Always plug in the power last!
Update: Also check your card if it's compatible using this list: http://elinux.org/RPi_SD_cards