hmmm from your description, it sounds like it might an ingrown hair. I’m a little confused, did the lump turn into the bigger purple spot or are they different? If it is an ingrown hair I suggest before trying to remove it, going to your GP to confirm it actually is that and not something severely worse such as an STI or STD. It could also be a cyst, which has to be removed by a doctor or if you’re brave enough yourself.
To remove, if hair however is to simply disinfect the area, get a sewing/embroidery needle or tweezers and try to pull it out.
There shouldn’t be that much blood. Also keep me updated, thanks for your message