I never had any stomach discomfort from fluoxetine when I was on it but generally speaking if a med makes your stomach upset then taking it with food will help.

As far as hiding it, if it is working properly then there really shouldn't be anything to hide other than the actual act of taking the pills. When it comes to taking the pills you don't relly need to worry about taking them at the exact same time every day with fluoxatine specifically. Fluoxatine has the longest half-life out of any SSRIs. The half-life of the medication is 1-4 days and the half life of it's metabolite is 7-15 days. So while you ideally still want to take it at the same time every day, practically it makes no real difference when you take it as long as you still take a dose every day and don't take them too close to eachother. It is the least picky SSRI as far as timing goes. If hiding taking the pills is a concern then you could even talk to your doc about switching to the weekly pill (because that does exist for fluoxatine).

Edit: Forgot you also asked about managing the other sideeffects. There really isn't much to do except ride it out and tell yourself it's temporary. Fluoxatine is one of the better ones as far as start up sideeffects go. I normally get horible start up sideeffects from depression meds and with fluoxatine all I noticed is that I was a bit more irritable for a couple weeks and at times I would randomly get a bit jittery for the first few weeks. Because of that last one it also seemed to make my caffeine tollerance lower so bear that in mind if you normally drink a lot of caffeine.