Hi Michelle - welcome to the support board...
The lump you describe is common with not only vaccines but just about anything that is injected through the skin (including antibiotics, allergy shots, depo provera, etc.). I had a VERY large lump (size of an egg) following a penicillin injection although I know that I am not allergic to penicillin. My DD had a red, warm lump following her 5th DTaP shot in the arm - was gone in a couple of days (we didn't do anything about it).
For some children, the lump represents just swelling from the muscle tissues being disrupted, capillaries leaking fluid, etc. - this type of lump tends to go away pretty quickly. The lump may also represent accumulation of blood - like a deep bruise - this can take weeks to resolve. Another type of lump is a local reaction to a vaccine component - typically one of the adjuvants or stabilizers that remains in the muscle and causes some irritation (oftentimes red and warm). Much more rarely, a child can develop a sterile abscess or develop a granuloma at the site of the injection - both are inflammatory reactions. With most of the types of lumps, they typically resolve completely in a matter of weeks.
Unless your twins had an immediate type hypersensitivity (allergic) reaction, then a lump is considered a mild reaction and would not be a contraindication to further vaccination. There is no indication that reactions like this get "worse" with subsequent vaccination.
HTH - Eve