Hi Allan
I'm assuming that your fields for your radiation treatment included to some extent your neck under your chin. Like others have said the stress of treatment and weight loss can cause low blood pressure which can lead to dizziness during postural changes ie. sitting to standing. This is due to the fact that your heart is a little weaker and cannot pump blood to your brain fast enough.
Radiation fields that include the neck can cause partial stenosus of the carotid arteries (vessel walls loose some of their elasticity) in the absence of low blood pressure this could be part of the problem.
The medical term for your dizziness is "orthostatic hypotension" you may want to google this to help you cope with it.
Some of my recommendations would be, drink lots and I mean lots of water to keep the vessels full. Yeah, you'll be in the bathroom every five minutes for the first few days but it will work itself out and your kidneys will thank you (quick fact: more than 50% of the population are partially dehydrated).
Next, when you plan to change positions let your heart and brain know. Stretch your legs, clench your butt cheeks, and tighten your abs a few times. These activities force the blood into your heart and brain which lets the heart know it has to work harder. Then slowly get up. Pilots do this to force blood into their brains to avoid G induced loss of consciousness during steep turns. Fighter pilots wear G suits that sense these changes and inflate with air to squeeze their legs, butt and abs to force blood into their heart and brain and help them along. By filling the pipes with lots of water and then doing the few movements I mentioned above you are basically creating your own G suit to force blood into your brain and eliminate and/or reduce the dizzy spells.

Hope this is a little helpful.

Take care,
Mike