At work today, my supervisor asked me to clean up an area near the tills while she borrowed my till to help a couple of customers with a refund. I was then asked to return to my till. After one or two transactions, I realised I'd been using her account instead of mine, after which I then signed out and logged back in onto my own account. She had forgotten to log out of her own but I'm worried that if this is discovered, I will be blamed for it. I wish I'd noticed she hadn't logged out before quickly enough to avoid the mistake. Now I'm scared I'll be fired and this isn't the first mistake I've made.

Explain to your supervisor what happened, don't try to hide of. Be upfront and honest.

I replied to someone's answer and then believed it wouldn't be helpful

She should have signed off her account. I see no reason for you to be blamed.
I responded to your other question. Please keep them together.
You sound nervous. Normal enough, but you can't get over that unless you stop this fear of being fired. You will or won't, but why bring it on?
Do the best you can, slowly.
You can smile at customers and say 'Bear with me; I'm new.'

I would assume, you called her and notified her at once, when you discovered you used her log in? If you didn't, why did you not do that.

But no this should not be an issue. If you are always scared and worried, then you will make more and more mistakes. You will need to calm down and just do your job.