I had the same issue and have finally resolved and figured out why... APPLE PLEASE LISTEN!
I have two separate apple IDs one for Itunes and one for Icloud. Only one of the ids is on my beta profile...and that is the problem!
This is what you need to do. WARNING you will loose all your data on your phone.
1. you need to remove your device from from Icloud under find my iphone.
2. You need to put the phone into recovery mode https://support.apple.com/en-us/HT201263
3. Set up as a new phone with just the apple id you used for the Beta
4. Go to beta and re-enroll your device and install your beta profile on your phone.
5. Go to software update and then Ios9.3 will show up
For some reason this beta will not let you use two seperate apple Ids.