Unless you happened to kiss this nurse (and I'm going to assume this was unlikely), her taking your blood pressure and removing an IV and putting a bandage on your arm would not transmit HSV (if this is what this sore on her lip represented) to you.
Please stop worrying about this and enjoy the upcoming holidays.
You indicate you and your partner used baby oil once but the condom did not break; thus even IF your partner cheated AND carried chlamydia he could not have passed this on to you during this one event with the baby oil used as lube.
' if neither of us have any symptoms is it okay for me to give him oral sex? or will I end up getting cold sores on my mouth and get it orally aswell? and the same goes for him?"
If you both have this on your genitals, there is a risk of picking this up orally. Will you? An internet forum cannot tell you this but this is a common virus, easily passed from one individual to another.
"if we both have it and have no symptoms of an outbreak can we just do everything normally the way we did before and not have to use any protection for anything? "
That's a personal decision between the two of you. Outbreaks are quite uncomfortable.
Because they just don't. No particular reason. This is why most folks who are infected are unaware of this and why it's a popular virus, both easily spread even when someone does not have an outbreak and even amongst those who believe they are uninfected.
And even after many years of education on the important of adequate protection with partners whose status is unknown, many will still engage in unprotected sexual contact, perhaps in the...literally..."heat" of the moment.