It is conceivable you have genital herpes, but certainly not 'definitely'. The transient pain on urination is an unlikely manifestation of an initial genital herpes infection, but conceivably could have been a recurrent outbreak if you are chronically infected without previous diagnosis. (Some people with genital herpes remain asymptomatic for a long time, then start having symptomatic outbreaks.) If so, conceivably you were the source of your partner's infection. However, most people with recurrent herpes have the classical external blister-like lesions and open sores.
A blood test ('titer') can show whether or not you are infected with herpes simplex virus type 1 (the usual cause of oral herpes and sometimes genital), HSV-2 (the usual cause of genital herpes), or both. There is no such thing as being 'exposed' but not infected. If a blood test is positive, you are infected with the virus, have the potential for recurrent outbreaks, and can transmit the infection to other persons. However, it takes several weeks for a blood test to become positive, so if you have a new HSV infection, it might not show up for a while.
To confuse the issue futher, your test showing 'initial infection' may be meaningless. Most likely that means your provider did an HSV test for IgM antibody. (The standard tests look at the IgG antibody class.) Although a positive IgM test is said to indicate a new HSV infection, in fact it doesn't work that way, and many positive IgM tests are false. But you probably will require additional testing (for IgG antibody) in the future to know whether you in fact are infected.
Most likely your out-of-state partner doesn't have it, based on her blood test result. (If you are infected, you could have infected her and the blood test will show it later--but that's not likely if she hasn't had any symptoms recently.) As I said above, people can have genital herpes for long periods without knowing it--so the fact that your ex-gf hasn't been very sexually active recently doesn't say much about when and where she was infected.
Another point: You don't say much about you ex-gf's symptoms. If she had a relatively minor outbreak--only a few lesions without a lot of pain etc--then she likely has a chronic infection. If her diagnosis is brand new and she presented with multiple painful lesions, lymph node inflammation in the groin, and/or fever or other systemic symptoms, then almost certainly she only recently acquired the infection. If that's the case, then you can assume you are chronically infected and were the source of her infection.
To put it succinctly, the situation is complex and there are several potential explanations about who is and isn't infected, when, and by whom. The 'by whom' part shouldn't matter; there is no point in playing a blame game--it doesn't appear that anybody was behaving irresponsibly. In any case, your best strategy is to find a herpes-knowledgeable provider who, applying a combination of clinical judgment and blood test results, should be able to determine whether you are infected and make recommendations to you and both your partners about future management, preventing further transmission, and the like.
I hope this helps. Best wishes-- HHH, MD
To the person who tried to post a new question: You have to use the Post a Question link. As many as 100 people try to ask questions each day and only a limited number (3-5, depending on how busy I am) can be accepted. The site opens up at random times each day. You have to keep trying. Anyway, nobody can diagnose anythhing on line. The only way to know what you have is to see a health care provider.
For information about IgM testing, use the search link and enter "IgM" and/or "herpes diagnosis"; you will find many discussions about it.
I don't get into speculating about causes of symptoms other than STD, and of course I cannot know which STDs you were tested for. If in doubt, return to the health care provider who did the tests.