Hi FussyEaterNY
Welcome to the club

It is true that some topical items like shampoo may contain wheat. I know of at least one brand that lists wheat in the ingredients. But I think you'll find that the vast majority of shampoos are GF. I use Citre brand shampoo and conditioner with good results.
About ingredients to avoid, the website celiac.com is considered a good source of information. You do need to avoid barley malt because barley is one of the grains that triggers the undesirable autoimmune reactions in people with celiac disease.
It is very common for people who are just starting on a GF diet to suddenly develop lactose intolerance as well. This is probably why you have heard about avoiding whey. In the usual course of events whey should be GF, but if you do develop lactose intolerance you'll be best off to avoid it. Cheese is most likely to cause a reaction in people with celiac disease who have also developed lactose intolerance - or so I am told. It seems as though many people are able to re-introduce dairy products into their diet after their gut has healed. This seems to take 6 months to a year for some people.
I generally eat foods that are labelled GF, or which I have determined are GF by reading the ingredients, without worrying about cross-contamination. Many other people with celiac disease are far more concerned about cross-contamination. It does seem that some people with celiac disease are far more sensitive to minute quantities of gluten than certain other people. Many believe it varies according to how much damage was done to your gut before the condition was discovered. It also seems that many people become increasingly sensitive to the tiniest trace of gluten the longer that they are gluten free.
It is generally accepted that an extremely small amount of gluten bearing food, like the tiniest bit of a bread crumb, is sufficient to trigger a reaction. I will not handle a wrapped package of bread, nor will I throw a leftover bread wrapper in the trash, without rinsing my hands immediately afterwards.
There is one school of thought in the celiac community that suggests you should personally contact the manufacturer of every prepared food item you intend to eat. Some even call companies that label their food as GF in order to ask for details about the manufacturing process, such as are other gluten bearing foods made on these same machines. Personally, I have not felt it necessary to do this. I have been GF for 7 or 8 years now, I know by heart what ingredients to look out for in ingredient lists, so I never consult lists of GF foods prepared by other folks. Many people starting out on the GF diet find such lists helpful.
Some things to watch out for:
Soy sauce is usually made with wheat. Read the ingredients. Currently I find La Choy soy sauce to be GF, and there is one slightly expensive Japanese brand we buy called San-J Wheat Free Tamari Soy Sauce that is truly excellent. Be careful with San-J, because some of their Tamari style soy sauce does contan wheat. Look for the bottle explicitly labelled as wheat free.
Hydrolized Vegetable Protein may be trouble. It depends on what vegetable source was used. In some cases it will be stated that the HVP is from soy, then it should be OK. Sometimes HVP is made from wheat, so if no source is listed you should avoid it.
You may hear some people say that vinegar is a problem. It usually is not. One type of vinegar you should avoid is malt vinegar, as it contains barley malt. Apple cider vinegar and distilled vinegar are gluten free. When a food product made in the USA says that it contains "vinegar" without saying what type of vinegar, then FDA regulations dictate that it should be apple cider vinegar, and it should be OK.
I'm sure you'll have questions as you learn the ropes. Ask, and we will try to help.
Steve