'If I'm not in pain I haven't worked out properly '
There is a difference between muscle soreness and muscle pain. It is expected especially when starting out that you will experience soreness the day or a couple of days after. As this is your muscles repairing themselves and thats ok. However it is also ok if you don't experience this - it doesn't mean you haven't worked hard enough. In fact it is more likely a sign of you cooling down, stretching and getting a decent nights sleep so your body is fully recovered. I know the main reason I wake up with DOMS (Delayed Onset Muscle Soreness) is because I sometimes don't stretch enough and I hardly get enough sleep.
Whilst working out you do want to be pushing yourself to your maximum effort so yes there are times where it might be a struggle and you may even feel sick! But you should never feel full on pain let alone work through it. If you are in pain whilst working out I highly suggest you stop and work out why. You shouldn't just push through it as you are likely to have or about cause injury.
As long as you are working your hardest and putting in 100% effort that is all that matters. You should come away from a training session feeling buzzed that you achieved it ... Not leave in agony because you hurt yourself. It's meant to be about feeling good in yourself, hitting PBs, smashing training goals and just getting fitter so keep that focus :)