Burning alone, without a visible outbreak of red bumps that become blisters, is not likely to be a symptom of herpes. Further, herpes symptoms are not likely recur as soon as a week; symptomatic recurrent herpes outbreaks just about never occur more often than once a month or so. It definitely is not possible to have on and off symptoms for 8 weeks.
And looking to your comments below, Valtrex cannot work so quickly. Even in people with overt herpes lesions, new lesions often continue to appear for a day or two after starting the drug, and symptoms don't start to improve until 2 days at the soonest.
Finally, you describe other very powerful evidence against herpes. Most important, the only kind of genital herpes you can acquire from oral sex is HSV-1 (because oral infections with HSV-2 are rare); and your own prior HSV-1 infection means you are immune, or at least highly resistant, to catching a new HSV-1 infection anywhere on your body.
So whatever is causing the feelings in your penis, it isn't herpes. Such symptoms also don't suggest any other STD, and you can be sure they aren't due to any infection you caught during the sexual exposure you describe. An HSV blood test probably isn't going to sort this out. It will be positive for HSV-1, given your oral herpes history. And even if positive for HSV-2, it won't explain your current symptoms; that outcome would just mean you have asymptomatic genital-area HSV-2 plus some other cause of the burning sensation. On the other hand, perhaps you would sleep easier if you knew you had a negative HSV-2 result. But the test pretty commonly gives borderline or false positive results, so you also risk ending up just not knowing one way or the other. However, feel free to follow through with that test if you wish.
In any case, you should stop taking Valtrex for sure and see a health care provider if the symptoms continue or you otherwise remain concered. But based on everything you say hear you have no worries about genital herpes.
I hope this helps. Best wishes-- HHH, MD