Others have already commented but I think the general rule of thumb is that if there is any noticeable change in behaviour/personality then a vet trip is a sensible idea. As others have said, African Greys are prey animals and therefore they are very good at hiding or masking illness. So when they start to show it, then it's definitely time for some assistance.
In regards to carriers, I have a travel cage that I use whenever I take Alfie anywhere. It's similar to this: King`s Cages Parrot Travel Cage Medium (premierparrots.co.uk) (You can get much cheaper versions nowadays too). I have space for a couple of perches, food and water bowls plus a small toy in there for him. I used to use a cat carrier but it was such a pain trying to get him in there and I never found a workable solution that didn't leave his feet covered in his own mess if he was going to be in there for a while. (I'm rubbish at DIY so adding a perch wasn't an option for me). So I splashed out on a kings travel cage (as that was the only make available to me all those years ago) and haven't looked back since. But I also use this for taking him to visit my parents regularly so it suits for much longer trips than just a vet visit.