Hi Simon
I'm pretty familiar with employment law, and from what you report very little law is involved here. That isn't surprising though, as this tends to come into play if your employer failed to follow any process or picked on you with no reason.
Losing your temper and throwing items that damage company property was rightly considered gross misconduct - no debate there. The only issue is whether your explanation is sufficient mitigation to allow them to drop the outcome to a final written warning (it couldn't sensibly be reduced further). However, this is a subjective matter - they were free to take it fully into account, or to pretty much ignore it - as they seem to have done.
It would help if you had a medical report to back you up, but even then they would run the risk of it occurring again. It does sound as though had you avoided 'frozen' this might never have happened. Energy drinks are not good if taken regularly, and these may not have helped.
Frankly, even if I were representing you, it would really rest on making a plea for compassion, and showing you were taking steps to eat and drink more healthily, and get treatment for any other conditions that might have made matters worse. And to be profusely apologetic.
Worth appealing, nevertheless, but don't try to justify what you did (you simply cannot), rather try to explain it through being unwell and how things will change. At the very least, try to get paid your notice, to give you a soft landing, even if you don't keep your job.
Sorry I cannot be more optimistic.
Best wishes.