Maybe the things that need dealing with first, are those affecting your head.
1) What brings on the headaches?
Is head position involved, i.e. looking down (head in flexion)?
If so, this is a common finding, so I would advise you to try and avoid this position wherever possible, i.e. carry out physical tasks sitting down, so the angle of the head is not as acute, keep paperwork at eye-level (books/kindle on bookrests, raise your laptop, etc)
Do you wake up with the headache ?
If it’s a headache you wake up with, it could be a cerebro spinal fluid (CSF) flow issue, due to the position of your head whilst sleeping. During waking hours our muscles help our ligaments to hold our heads, however during sleeping hours, we do not have the benefit of muscles working and so, we are more or less reliant on our ligaments to hold our head in a good position. If you have the stretchy type of EDS, this means the ligaments that hold ‘your head on’ could be stretchy too, do you get what I am saying ? Many sleep in a rigid cervical collar to help with this. It could also be circulatory (due to malfunctioning autonomic system), many of us sleep with the head of the bed elevated. I actually sleep sitting up.
Is the headache there all the time ?
It could be worsened by lack of oxygen in the room, every day ensure you get a ‘change of air’ in the bedroom and any room that you spend a lot of time in (even if you have to wrap yourself up in at coat and gloves while you have the door full open for 10 minutes!).
Can you describe it ?
Is it an acute pain at the bottom of your head (often felt in those with CSF flow issues), especially if it also affects your neck and shoulder, if so, you may need to wear a collar during the day too, to help keep your head in good relationship to your neck and assist in optimum CSF flow.
Useful medical tests would be:
Cine MRI – to check for CSF issues
MRI – to rule out other causes and to check for the things I highlight in the following post
2) What brings on the dizziness ?
Just as there are various descriptions of dizziness, there are various causes, e.g.:
Disorientation – where you’re suddenly mentally ‘a bit lost’, usually momentarily
Lightheadedness – like the feeling before your going to faint
These can be brought about by vascular issues, like insufficient blood to the brain for instance (maybe the blood is fighting to get in, against raised intracranial pressure).
Vertigo – where your surroundings appear to be moving, when in reality they’re not
This can be caused by raised intracranial pressure, affecting the nerves controlling the balance mechanism.
Useful Medical Tests would be:
Neuro-opthalmologists assessment to look for Swollen Optic Disk (sign of raised intracranial pressure). If found, then a course of Diamox should help, it certainly did for me.
Neuro-otological assessment to look for any other causes
You can perhaps address these as a starting point.