Scott,
If you read the primer on this website, there is a section o diaper stigma, and the euphemisms that manufactures use to sell products for us adults.. if you are afraid of offending members on this site..don't be.. Many of us have come to grips with the realities of incontience.. and use the words diaper, brief, and protection interchangeably, at least I do..
As far as briefs vs pullups.. I doubt you would find a pullup more absorbent than a tape-on brief/diaper. I'm assuming the diapers you bought at CVS are store brand? In my opinion, store brand briefs are not worth the packaging they come in..they are about as thin as paper..The most vunerable positon for a diaper to leak is sitting down.
I have moderate to heavy stress/urge/overflow(i think????not sure) incontinence, and for daily home use wear Attends breathable.. and when im at work or a situation where i cant change easily.. i wear a premium extended wear brief, such as Dry 24/7, Wellness, or Tena slip Maxi. I think that you will find that you have a MUCH wider selection of protection choices online, and having boxes of diapers shipped to your house is more discreet than buying them in the store.. me, personally, i only buy locally at the phamracy near my building.. otherwise,I just feel weird doing it.. thankfully.. my supplies are covered via Medicaid and i get a monthly shipment of everything i need for management, including briefs, wipes, rash cream, booster pads, and chucks pads for airing out.. all at no cost to me

My incontinence first became noticable or bothersome . I got dry in early 2010..now its back 4 years later.. first reoccurance was in May, saw the urologist, did biofeeback and excercises.. was dry late july through late septenber.. then started having leakage up until now. It was difficult at first to come to terms with having incontinece come back, but acceptance for me has gotten easier with time. I'm glad you don't have a problem wearing protection, beacause it really does make life SO much easier.. when things stared prior to 2008.. id have the occasional postvoid leak.. which became more routine.. and for the longest time i put up with wet undewear.. NO MORE. I either wear underwear and keep them dry.. or wear diapers..no in between...
Welcome to the forum.. I'm sure you can find a lot of stories you can relate to.. and don't forget, we are all in this together!
Peace out!
Rob