The "lumps" you describe on the eggs are I think calcium pips. Here's a photo of what they look like. The lumps are formed from small pimples of calcium which somehow have not been deposited evenly over the egg. If they are rubbed they will disintergrate into tiny calcium beads and fall off leaving a chalky rough shell. They are nothing to do with worms so far as I know.
The shells of such eggs are usually gritty or chalky and can be thin. The egg shell is secreted by glands in the uterus and this condition can be caused by excess of Vitamin D3 causing excessive calcium absorption, or by heredity factors and is not generally associated with a disease. Older hens are more susceptible than younger hens. If you are feeding a calcium, cod liver oil, tuna or multivitamin supplement I'd stop doing that.
The photo shown was an egg produced by a 3 year old Sussex chickens. Such egg shell problems including thin shelled eggs often follow a moult when a chx body chemistry is returning to normal and is usually a temporary condition.
Signs of worms apart from finding them in the droppings are thin birds, weight loss while feeding well, foamy yellow / green droppings, pale head, droopiness or depression, reduced eggs. Gapeworm symptoms - coughing, gasping, yawning, closed eyes, head shaking.
Worming - it is generally advisable to alternate wormers annually to reduced worms resistance to the wormer.
Flubenvet is a very effective wormer against many species of worm whereas I've never seen evidence or any scientific trial data which shows VermX which is basically expensive garlic to be effective. Even the manufacturers publicity seems not to express a great deal of confidence since it also recommends regular testing for worms even in treated flocks. I can't recall what it recommends if worms are found but probably to switch to an effective wormer! I do know that VermX were forced to withdraw claims in it's advertising for the universal effectiveness of it's wormer by the Advertising Standards Agency in 2009 because of lack of evidence to justify their claims. In fact the case related to worming horses and only evidence it provided I seem to recall was a student thesis study which I'm not sure was ever published in a scientific journal. Anyway the ASA weren't too impressed.
Never heard of using cayenne pepper as a wormer nor do I place great credence on the anecdotal evidence cited for it's effectiveness. How could we know that the lack of worms is down to the pepper and not some other factor such as control of intermediate hosts (insects), good sanitation, being raised on wire, feed, or other medication they were receiving, or climate related, or chicken breed. A scientific test would involve a control group of identical birds which were not treated with the pepper but otherwise treated identically with the peppered chx. If they showed signs of worms whereas the peppered ones were free then that may be the basis for a story. It's a bit like the white powder I sprinkle to keep elephants off my birds. When I'm told "but there are no elephants round here", I reply that the powder is very effective.
Think I'll stick with Flubenvet for the present.
HF