Thank you for the additional information.
First, there is no reason to be concerned about STDs because of these symptoms. However, to address your first question, yes, it is possible to have an STD despite a negative test. Although the antibody blood tests are very accurate, the tests to directly detect germs, such as gonorrhea or chlamydia, are not perfect. The accuracy of the current generation of tests are very good, generally better than 99%, but in someone with worrisome symptoms, doctors may still be concerned about these germs. This would not apply in your case, since these symptoms are not worrisome for STDs.
As for these symptoms, it is very unlikely that these are any type of infection transmitted during the encounter of oral sex and it is more likely to be some type of reaction, most often an allergy. When germs are transmitted from one person to another, it will typically take at least a couple days, and frequently longer, for the germs to grow in the recipient to then cause an infection. However, symptoms that arise because of a sensitivity can arise much more quickly. Symptoms that arise within a day or two would most likely be due to a sensitivity to something to which there is exposure. It certainly is possible that once there is inflammation from a sensitivity/allergy, a secondary infection can develop over a few days.
The most common substances to which someone can be sensitive during oral sex are substances that are left on the genitals as residual from cleaning, such as in personal soaps or laundry detergents residue left from clothing. Perfumes and scents also can be an issue, although these are not as often applied to the genitals.
You can try to eliminate or change the common substances to which people can be sensitive, such as changing soaps and laundry detergents. It also would be reasonable to try an antihistamine taken before an encounter of oral sex to see if it can prevent symptoms.
If I can provide any clarification, please let me know.