Can HSV-1 Be Asymptomatic?

A little over one month ago, I contracted HSV-1 from my former partner. He had a cold sore on his mouth and he preformed oral sex on me. I got a few cold sores inside my mouth (nothing too visible, just small and painful), and two blisters on my chin. On the lower region, I had a few painful bumps around the opening. I saw my gynecologist, and I went on medicine to get rid of them. They disappeared in four days. Now, every single night since I had the initial outbreak, I am taking 500 mg of valacyclovir (prescribed) and a pill of lysine (that I got from the vitamin store, recommended by my gyno). I have this new boyfriend that I really like, and I don't want to have the "herpes" conversation with him. We had unprotected sex and I gave him oral sex three times last week (when I wasn't having symptoms- I am sure to carefully examine myself before we have sex). However, now we are using a condom. I casually asked if he had ever gotten a cold sore before and he said no (so I'm assuming he does not have HSV 1 already). I haven't noticed any bumps on his private parts. He also said he has not gotten a fever or anything like that, which is common when you get the first outbreak. However, he does have a scab/rash coming out of one of his nostrils. I asked what he thought it was and I asked if he thought it was blisters, and he said he didnt think that is what it is, he thinks it was just a cut, and he is seeing a doctor.
1) how possible is it that I only gave it to him on his nose (without me having any symptoms) and not on his genitals?
2) how possible is it that I gave it to him both places and he has only had symptoms on his nose?
3) how possible is it that I give him HSV 1 at all if I am without symptoms?
Also, how possible is it that I am shedding the virus one month after my initial outbreak if I am on suppressive medicine, its HSV1 on my genitals, and I take lysine?
Also, I have been reading about what its like to have outbreaks, and i read about tingling, and now I feel like I have the slightest amount of tingling and itching down there very occasionally. I'm not sure if its in my head, if its the humidity, or if I'm about the have an outbreak. Would the tingling be distinguishable, and would the blisters appear right away? its been going on for a few days (pretty minimal, I am just hyperaware of anything going on down there now) and no blisters have appeared on my genitals. I look twice a day very closely with a mirror.

Please help!!!! I am worried my future relationships will be ruined.