Hello, the other expert has opted out.
There are a couple of common possibilities in this situation.
First, it is possible that this is inflammation that is occurring as a reaction to something to which the penis is coming in contact, which could be the new body wash. This would be a type of allergy, so a reasonable first step would be an oral antihistamine.
Discharge and redness of the opening of the penis also can be due to an infection of the urethra, the tube that opens at the tip of the penis. The greatest concern is that this could be a sexually transmissible germ, such as chlamydia or gonorrhea, although there are also some other germs that can also be present. The fact that your current sexual partner does not have any symptoms does not preclude the possibility of such an infection, because these germs can be present without causing symptoms. So, it is possible that you have been carrying the germ for a while and is only now causing symptoms or that she has been carrying the germs and has never caused symptoms for her.
If you take an oral antihistamine and it eases symptoms, then that would support that it is a reaction, and if it resolves and does not recur, then no further evaluation is necessary. Of course, if you are sensitive to this body wash, then it will also be necessary to stop using it. If the symptoms persist despite antihistamines, then it would be appropriate to be checked for infection.
If I can provide any further information, please let me know.