First, be sure to report that reaction to your vet. Hopefully you did so at the time it happened, but be sure your vet documents it in the patient record. Then, ask your vet if they are following the AAFP (American Association of Feline Practioners) guidelines for feline vaccination. If they say no (or don't know what that is), find another vet.
http://catvets.com/professionals/guidelines/publications/?Id=176
The PDF:
http://www.catvets.com/uploads/PDF/2006%20Vaccination%20Guidelines%20JAVMA.pdf
No core feline vaccine should be given near the neck. FVRCP (upper respiratory viruses) is typically given low on the right shoulder and is only needed every 2 - 3 years. The other two core vaccines are given low on the right (Rabies) and left (Feline Leukemia) rear legs. Rabies frequency is legislated by your state. Feline Leukemia (FeLV) is only necessary if your cat has contact with unknown/unvaccinated cats, specifically sharing food, water and elimination resources. So if your cat is strictly indoors and has no contact with any cats that go in and out, it does not need FeLV.
You should be able to request a few things to help minimize side effects/reactions.
1. No unnecessary vaccinations. Some vets give multiple vaccines every year, and, to be honest, this is just to jack up your bill. It also increases the risk they will have a reaction. Give them what they need, but not more than they need.
2. Separate vaccines. There are situations when a cat is due three vaccines in one year. We try our best not to give more than two vaccines at a time and separate the third one by 2 - 4 weeks. If it makes you feel better, you can even ask to separate all of them and only get one at a time. YOUR VET SHOULD NOT CHARGE YOU ANOTHER EXAM FEE. They should do a thorough exam the first time and basically just check a weight and temperature before giving the vaccine on subsequent visits.
3. Premedicate with a benadryl injection. Cost should be minimal and they should give it about 15 - 20 minutes to kick in before giving the vaccine.
4. Change the needle! Ask your vet to change the needle on the syringe after drawing up the vaccine before administering it. That needle has already been through two thick rubber stoppers and is now DULL. A sharp needle will be more comfortable and cause less physical trauma for your cat.
I recommend the above for everyone, but for you specifically, find out exactly which vaccine your cat reacted to and see if it's not one that you can simply stop getting. If not, be sure to follow numbers 2, 3 and 4 above. If the lump happens again, make sure your vet documents it in the patient record and never get the vaccine again. Especially see "Vaccination of cats with prior
vaccine-associated adverse events" in the link above.