Can itching and swollen penis be symptom of reaction to amoxicillin?

Dear Rocky Dog... I see that this question was posted about 2 hrs. ago so I am hoping that you have already taken your grandson in to a Minor Emergency Clinic, Minute Clinic, or ER. If not, please give him a Benadryl, depending on his age (read dosage instructions) and then take him in to be seen by a medical professional. If not Benadryl in the house you can also give him another type of antihistamine like Zyrtec or Claritin. Benadryl is the prototype but the others will work alternatively.
Allergic reactions present themselves with hives, itching, and swelling... the swelling is usually of the airway in many cases but occurs all over. Not that the penis unimportant, but your grandson was lucky that he did not have swelling of the airway. In any event he still needs to be seen by a medical professional.
Histamine is produced by the mast cells in our bodies. This is why antihistamines are used to treat allergic reactions. The classic response is the response of your grandson. It occurs on the second occasion that the antigen (antibiotic in this case) is introduced to the body. On the first occasion it is introduced the body builds up antibodies to arm itself for defense for the next occasion this unwanted drug enters the body.
If someone has this response on the first time the unwanted substance is taken it is really not a classic allergic response... it is called an idiosyncratic allergic reaction. This is just an FYI... it is still serious nonetheless.
Your grandson will not EVER be able to take penicillin again, or any of it's derivatives... Nothing with "cillin" at the end of the word. Some antibiotics may not have "cillin" at the end. The pharmacist and doctor should tell you this. For example, Augmentin is a penicillin without the "cillin" at the end of the word. It is amoxicillin combined with clavulonic acid.

I am sorry this is longwinded. I seem to be in a teaching mode today.
"Allergies" tend to be my soapbox because so many patients come in and say "I am allergic to such and such" when their symptoms may be nausea, dizziness, etc. to a drug when the symptoms they describe are usually an untoward and unpleasant reaction to a particular drug. One very common response that I get from patients are that they are allergic to Novacaine in the dentist's office because "their heart 'pounds' or 'beats fast' after receiving a Novacaine injection. Dentists use epinephrine mixed in with the Novacaine to reduce blood loss in the oral field where they are working to repair a tooth. This is a normal reaction if the Novocaine with the epinephrine is inadvertently uptaken by the blood vessels in the mouth, hence a response to the epinephrine of a "pounding or fast" heart rate. Dentists are notorious for telling patients that they are then "allergic" to the Novoacaine, when in reality, it is a normal reaction to the epinephrine.
Anyway my friend, thank you for allowing me to "educate" a little bit about allergic responses to drugs.
Allergic reactions are a very serious thing, not to be taken lightly. The most serious allergic response is a full blown allergic response called anaphylaxis. This is when so much histamine is released by the body that it causes massive vasodilation of the blood vessels and massive swelling of the airway to where the patient will go into shock and the airway becomes so swollen that it causes obstruction and therefore unable to get oxygen into the body. This could happen if your grandson takes any penicillin of any kind again. Your grandson, from now on, should wear a Medic-Alert bracelet alerting anyone treating him that he does in fact have a penicillin allergy.

OK... I hope this has educated you or anyone else who might be reading this regarding allergic responses to medications, or for that matter, other substances ingested, i.e., ant bites (Formic acid), peanuts, shellfish (iodine), etc.
I hope that by now your grandson has been treated and is now on his way to recovery.
All my best to you my friend. Have a wonderful rest of the weekend...

I suggest you take your grandson to the ER ASAP, he is having an allergic reaction to the antibiotic.

All the best,