Pretty much herpes sores are prodrome (warning signs, like tinging, if you get them), then blisters.
Prodrome can last up to 2 days. Prodrome, if you get it, is always followed by an outbreak. If you get tingling or something that lasts for days, with no outbreak, that's something else and not prodrome, or herpes.
Why don't you just go to an urgent care or walk in clinic or whatever it's called where you live, and get this looked at? You aren't going to rest easy until you do. If they think it's herpes, ask them to do a type specific culture or PCR swab (if they can do a PCR swab, that's the better option). Insist on that. Don't let them visually diagnose you with herpes - it's wrong a lot of the time.
Don't wait - the sooner you can go, the better. It's not worthy of a trip to the hospital, but if you can get to an urgent care today, or tomorrow, do that.
If the cut on your tongue is really similar to biting your tongue, that's probably what it is.
In theory, you can transmit herpes by fingers like you suggest, but it's just really an inefficient way to do so - it's exposed to air and such, and the mouth doesn't like hsv2, and hsv2 orally is rare. It's not something I'd worry about.
I would be concerned that you have transmitted your cough to her. Maybe don't have sexual activity while you're sick. :) If your cough lingers for more than a few more days, see your doctor for it. Feel better!