This question is more about social interaction than language use.
Think about how you'd express your "real sympathy" in your native language. There are socially accepted formulas in every language and every society and culture, but your "true feelings" are expressed more by the tone of voice and the body language that you use rather than the words (unless the words are obviously inappropriate for the occasion).
If someone else's mother's been hospitalized for an illness, That's too bad isn't the best expression. I'm really sorry to hear that plus, perhaps, I hope she'll recover quickly is much better. Stick to the formulaic if you can't come up with a spontaneously appropriate expression.
My son, a native speaker of Chinese, not really a native Anglophone, says too bad all the time. I find it annoying, but I think he learned it from me. I use it for stuff like having to work two weeks straight without any time off and other unpleasantries of everyday life, but never to express sympathy for sickness or death or anything else that's serious.
Although it's difficult to say "Too bad" without sounding sarcastic, it's possible. I wouldn't advise it, though, because it's too terse, too curt, to be sympathetic. "That's too bad" is a little better, but, depending on your tone of voice and body language, it can express sympathy, but it's not the best way to be taken seriously by someone who's grieving about a loss or an ill relative.
Neither of these phrases are appropriate for what you are trying to express.
To fool someone means to deceive them, so saying that you "fool yourself" would mean that you are tricking yourself into believing something that is false.
The phrase "fake myself" sounds odd. It would be better to describe the state that is being falsified, e.g. "fake confidence."
In my opinion, other words are better used to describe this situation, many of which you used in the body of your question. The verb "act" implies that one is faking. To say that you are "hiding" your true emotions is also a valid way to express this. Here are some more suggestions:
I acted strong despite my weakness.
I chose to hide my anxiety.
I smiled with manufactured confidence.
I responded with optimism I did not feel.
I tried to cover up my mood with pretend cheerfulness.
(Note that "pretend" is used as an adjective in my last example.)
Another word you might consider is "feign", as in "to feign confidence".
Best Answer
Be careful about "don't bother", it can be interpreted as actively hostile.
It's about like when you say to your other half, "I'm going to spend the rent for the next 3 months on a new motorbike", and she (sorry, it's usually "she" in this context) says "Fine!" when she really does not mean "fine", what she means is "I'm obviously not going to be able to stop you doing whatever immature selfish thing you like, but if you do, then our relationship is over."
In this case, "Don't bother" means "It's obviously far too much trouble for you to just perform this minor courtesy for me, and I clearly cannot rely on you to pull your weight in this relationship, so please be aware that our relationship is on shaky ground as of now."
So if someone offers to wait for you, and you say "Don't bother", it can be interpreted as a rude rejection of a courtesy offered, and the person asking would spend considerable emotional energy wondering what it is that he or she has done to upset you.
Better would be:
"Thanks, but you go on ahead, I'll catch you up later."
Then there is nothing in what you said that indicates that there is any sort of obligation that you need to be waited for.
Even saying "thanks, but you don't have to" is using the language of obligation and duty ("Have to") and can cause awkwardness.