I've gotten sick/injured on the job three times in seven years.
The first was in a hotel in CID, I had an allergic reaction to something, (still have no idea what) and my eyes swelled shut during the night. We weren't due out until around noon, so at 8am I called scheduling and told them about the situation, which gave them enough time to find a reserve and get them on the inbound flight. The flight I was supposed to work was not delayed or affected in any way. I called my captain so he would know what was going on, and he was kind enough to accompany me to the emergency room, where I got treated and was actually on my way back to ORD before the rest of my crew!
The second time was when we'd arrived in PIA for the overnight, the ramp people were busy with the aft cargo, (all the pax were in the terminal by this time), and the crew bags were in the front cargo. So, nice person that I am, thought I'd get our bags out of the front cargo. The fwd cargo door on the ATR is easy enough to operate, but when fully opened there's a hinged strut you have to push on to support the weight of the door, and in pushing that strut my thumb got smashed between the strut and the side of the airplane. I was pretty sure I'd broken it. I didn't say anything to anyone about it right away, instead I went to the hotel, sat with my hand in a bucket of ice crying on the phone to Bill until at 2am he finally convinced me I need to go the emergency room. So the hotel van driver took me in, turned out it wasn't broken after all, just very badly bruised. (But I did lose the nail..yuck) I called scheduling around 2:30 and since we weren't due out until 2 in the afternoon they had plenty of time to cover it.
The third was coming out of BNA with AA. We had a fairly early morning flight back to ORD, and I hadn't been feeling right ever since I'd got up. It got worse, but by the time I was feeling really bad, we were already airborne and it was too late to do anything about it. So I served first class breakfast, threw up a few times, managed to make it through landing, but had to disapear into the lav again as soon as the door was opened. The pax never knew anything was wrong. I'd told the crew inflight I wasn't going on to PHL with them, and I called scheduling as soon as I got to the crew lounge. Since this was in ORD where we have a crew base and airport standbys, this was no big deal. There was another FA ready to take my place within a matter of minutes.
So, sorry to ramble, but if you know you're physically unable to adequately perform your duties, just do yourself and the rest of your crew a favor and call in sick. Try to give as much notice as possible to scheduling, if you are at an outstation they can get a reserve on an inbound flight. If you make a sincere attempt to call as soon as you know you're sick, that's all the company can ask. Try not to make it a habit, but you gotta do what you gotta do.