Hi and welcome,
Your question has landed in the MS community but bleeding and swollen gums is very common and typically caused by bacteria not being removed by your oral hygiene routine or technique, often all that's needed are minor changes eg using an anti bacterial mouth wash, replacing your tooth brush every 3 months, changing to a soft bristle tooth brush, brushing more softly, altering your flossing routine, brushing in a circular motion, brush at about a 45 degree angle, eating a low-sugar balanced diet; drinking plenty of water etc
Woman can also experience this more from fluctuating hormones, hormonal changes can alter a woman’s response to oral bacteria and increase blood flow to the gums, causing bleeding during brushing and flossing. Mental health medications and other types of medications can also cause oral side effects so it's worth checking if any medications or over the counter medications could be involved. Another thing to consider is changing your toothpaste, many tooth pastes now have a whitening agent which you could be reacting too.
The burning pain on the top right side of your head that worsen when you turn your head to look to the left, if it's not headache or migraine related, sounds like it 'might be' something like occipital neuralgia....basically there are two occipital nerves in the spine of your upper neck that runs up to your scalp, usually the nerve pain (shooting, electric, burning or tingling) will be on only one side of your head, and in most cases, neurologic exams will come back with no abnormalities.
Occipital neuralgia is most commonly caused by pinched nerves in a person's neck, sometimes it's related to the muscles being temporarily too tight in a person's neck or chronic neck tension. Consider things like your postural behaviour from too much time holding your neck bent forward with your head tilted down whilst looking down at your computer, tablet, mobile, book, hobbies, game console etc stress and anxiety can also cause the muscles in your neck and shoulders to be too tense...generally warm compress, basic relaxing exercises, massage and behavioural changes during activities will resolve the issue but sometimes medications like a muscle relaxer and or tricyclic anti-depressants and physio are needed.
I'd recommend you first consider if there are any behaviours your doing that could be irritating-pinching the occipital nevers in your neck, as well as consider your mental health situation may be part of the problem but IF there are no cause and affect aspect to why it's happening then you'd best see your GP and get it checked out.
Hope it helps.......JJ