Hi Sarah - I can't pretend that I've recently done my first race (mine was a little over five years ago) but I do recall some of the feelings, many of which have repeated themselves to varying degrees at every race since including one last night which was my first race back after an injury layoff. I too am building back up to other races so it felt a little like your 10k will feel to you.
Before your first race you can expect to feel excited but nervous (bordering on terrified for some people). This is entirely normal. You may struggle to sleep the night before - this is normal too as is the possible feeling that somehow you 'don't belong' (this usually brought about by the sight of knots of other runners all wearing club vests and looking like they know exactly what's going on - for many, its an act - they're all nervous too).
After the race, the most likely feeling will be that it went far better than you feared/expected. Assuming your training has gone well, you'll either have finished quicker than planned or feeling like you could have gone faster - that's fine too - you now have a PB to aim for and, probably, a medal to show off with. You will, almost certainly, not have finished last. Enjoy it.
I've seen another of your threads and the advice there is sound - build up gradually and you'll be fine. Use a schedule geared towards the half marathon and use the 10k as a chance to experience the race atmosphere and check where you are up to - doing that 10k as part of your build up is an excellent idea. Similarly, Mr Moonlight's point about running YOUR race rather than anybody else's is spot on if easier to say than do - the 'mistake' you're most likely to make is to go off too fast then crumble towards the end and finish feeling like a wrung out dishcloth - even if you do that, take time to reflect on what you've achieved (treasure the medal) and where you've come from before putting it down as a lesson for the future.
For me - last night, I picked a small local race with plenty of hills - I finished further back than I would have hoped to if I were fully fit, and behind some names that I know I've beaten in the past. The race itself was hard work but I trusted my training and the race confirmed what I thought - I've retained some basic strength but need to do some more speedwork!
Hope that rambling is some sort of help