You're not going to get rid of the feeling of anxiety without the tablets. No amount of thinking and planning and timing when you take the tablet will make that anxious feeling go away, so you need to stop trying to do that. The anxious feeling is completely out of proportion to any real risk (which is why you've got the tablets) so you need to accept its presence (until the tablets work) rather than trying to get rid of it before you do anything else.
Well done on going to the bbq despite the anxiety. If you can just do the same with the tablet, you'll have taken a step towards properly getting rid of the anxiety
But give up on trying to get rid of the anxious feelings, give up on waiting until you feel OK about taking the tablet to take it, or you never will. You know you need to take it despite feeling anxious about it so grit your teeth and try to make yourself do it anyway.
The number of times I've postponed taking medication for exactly this reason is ridiculous. I've never had any kind of instant reaction, or even bad side effects in general.
You might feel quite relieved once you've taken the first tablet and discovered that nothing bad has happened straight away as that will be one less thing you need to worry about.
Can you just make your hands move faster than the worrying part of your mind? Just grab the packet, take out a tablet while going 'la la la not listening' and swallow it fast? It really is the only way - because you have anxiety as a problem, trying to push away the anxious feeling first is like trying to stuff a duvet into a sock - impossible, however much we reassure you or you try to make the timing perfect. So taking the tablet despite feeling anxious about it is the only way, and it might as well be today.