The dictionary defines guilt as committing or being implied as committing an offense or crime. That's a sweeping brushstroke that colors that word.
The dictionary defines shame as a feeling of humiliation or distress by the consciousness of wrong or foolish behavior/actions.
When you have an invisible illness, both a sense of guilt and shame are not uncommon companions. I know for me, for the longest time, I felt guilty about having to cancel on friends, school, work, and so on. I also felt tremendous shame at being a horrible friend, unreliable student, and perceived as an irresponsible employee for calling in sick.
Sure, my friends understood and accepted that I might cancel plans at the last minute. My friends also knew about my illness and were supportive. I was blessed to have understanding professors and employers.
There is no reason to feel guilty about needing to rest or not be able to do something one day. There is no reason to feel ashamed of being ill. It can be hard to change how you view things, especially when you feel like people see you asking for special privileges.
Consider this:
Forgive yourself for feeling/believing that you are not equal to your healthy peers.
Choose to believe in your worthiness, in being okay with resting when you need to rest so you can be your best later on.
Proclaim the strength of your knowledge, knowing when you need to bow out of something and when you can step up.
Embrace how amazing you are as a person, how you manage to step up and live a full life while managing your illness.
Feel free to let those feelings of guilt and shame leave you when you exhale deeply. You shouldn't feel shame or guilt around your illness.