flip the situation round - imagine you're very sick (sex might be literally impossible but assume you're too weak to want it anyway) - imagine she's the carer ..
would you tell her to go and have an affair? that she should leave you cos you can't be a "true" husband any more? or would you expect her to adapt to the changed circumstances?
adapt I suspect!
but don't beat yourself up : you have tried to adapt and have resisted an affair. and being honest about your feelings is more likely to save your marriage than hiding them.
Sounds like you were close, but now are not: making conversation difficult.
Counselling might help: stop you both being entrenched within your own perspectives and provide a neutral environment. Your wife is much more entitled to the sympathy vote as she is ill, but if you as carer feel martyred and unloved (because no affection, let alone sex, the marriage may crumble tthen no-one - your son included - wins).
Affection, seems reasonable to express your wish for this at least? (a cuddle, holding hands etc) - perhaps she resists because she thinks you will then want sex (which she does not want)?
Sex - she needs to feel sure enough in your ongoing support to be honest, seems fair if you wish to express the distress you feel, even if it does not distress her .. given it was (presumably very important to you both before).
Your situation is a very difficult one for all of you, and I think one where the normal idealised rules might be better off slightly bent if it saves your marriage and keeps your family under one roof.
You will know your wife best, so will have a view as to how open you can be about your physical needs. Posts on this site are only ever about OW - DH's who seek sex/intimacy outside their marriage which the OW then threatens.
I suspect there will be DH's out there who would quietly take you on one side and tell you to "pay for it". To keep emotion out of it avoid an OW who will get emotional and will say this compromise saves more marriages than you think. I don't myself know any DH's who admit to this- and as a woman/outsider it is hard to understand how that could be a good or appealing idea - but it must go on. DH's view needed here.
The majority of women people will berate you as a selfish , BUT that kind of comment won't actually help you or your wife as you do feel guilty, as well as being terribly unhappy, already.
Be kind to her, and as kind on yourself as you can be. Find whatever way you can to keep your family together - it'll be very hard work, and will need compromise (on both sides). If you're a decent guy you'll never feel good about yourself deep down if you abandon her. She probably would not have abandoned you if you were the ill one.