I think the chances that you have HSV 2 and had not serconverted yet for HSV 2 are low. I would say you have at least 90% certainty at 3 months that you do not have HSV 2. Did you take antiviral medicine? If yes, for how long?
And no, I don’t think there is much chance that he got infected from you by doing what you did. Has he actually been tested for HSV 2? That would be important to know before you go much further with this, I think.
There is no point in having your mouth swabbed for HSV 2. If you happened to have HSV 2 orally, which is not common, it is only shed on about three days of the year. Random swabbing of any location without lesions one time only is rarely productive. I think just getting another IgG test for HSV 2 is plenty if it has been 16 weeks since possible exposure.
The HSV 1 positive test result that you had could be from infection orally or genitally and you could have had it a short time or a long time no way to know if you have never had a cold sore on your lip. You may wish to get the nose thing swab tested by PCR.
Terri