If the screening is a CT scan then that is the one I had. The CT machine is like a big donut, you lay on your back and it only takes a few minutes., waiting for the test and the results is actually the worse of it all. I, like you have issues with enclosed places, but this one wasn't so bad, but I concentrated on wiggling my toes (which you ask the tech if you can of course) and keeping my eyes closed. Once you are in the machine, a voice will let you know to inhale and hold your breath, then of course to breath again, that is really fast too! Another option you could contact your doctor, let him/her know you have issues with being in tight places and they will usually be able to prescribe you one little pill to relax you for the test, I use this for MRI's and other tight places they choose to put me every so often. This of course will be explained to you when you get to the appointment, all the people that do these types are tests are very sweet and will try to help you relax through it. It is a fast test, probably about the same amount of time as a mammogram takes., for an example.
Here is a link I found, about 1/2 way down the page on the right, you will see a person in the CT machine for cancer screening, hope this helps ease you a little
https://www.cancer.gov/about-cancer/screening/screening-tests
Yes, cleaning and cooking is something I can still do some of, but nothing like I use to and truly not as fast for sure. I do understand as many on here just might also. It's great that your dear hubby and son help out, some of us are very lucky to have the extra help available. As for laundry, I still help switch loads over from washer to dryer and later fold them of course for that is much easier and need to keep those arms moving! You forgot doing dishes! I love standing if I can to wash them, makes my hands feel so good from the arthritis.
Will keep you in my thoughts and prayers for a clean screening!
Best of luck to you,