It fell from a short height, but it fell backwards, so the drive hit the floor and then everything else.
When i turn it on, it makes some grinding noises but it's very quiet, i can only hear it if i put my ear next to the drive.
It works very slow, and takes a while for my desktop to show up, as in it turns all black and then slowly my taskbar comes.
Nothing is broken from the exterior, but I'm still worried as to it being very slow.
Is there a way i can fix it at home?
My laptop is an Asus, model:TP300L PC notebook
Most likely thing that will happen, is that your HDD is the only thing that will be mostly affected. Unlike SSD, HDD has mechanical moving parts, so a fall might ruin it.
Others things/parts your laptop ( like the LCD, if not damaged/broken) should be mostly fine.
If I were you, I would get an external HDD and quickly make backups of important files or datas. Then if your old HDD is damaged, I would simply replace it with the new one. Replacing HDD is one of the easiest thing to do to most laptops. The guides for that is pinned on top this forum.