You'll get used to it and eventually it shouldn't trouble you, so you needn't worry.
The advice I got was to keep the cockpit cool, ensure good air circulation and just try to keep your mind pre-occupied with thoughts other than "oh no, I'm going to feel sick". I know it's difficult, I've been in the same situation. The other thing to do is if you're feeling a bit nauseas, ask you instructor to allow you to take control of the aircraft and fly straight and level, and fixate your sight on a stationary object outside.
Avoid moving your head too much whilst you are banking, once you are banked an set up in the turn then you can move your head around for look-out.
If you are flying on instruments only then ignore any illusions and what your body is feeling, and in effect over-ride those senses and believe soley on what your instruments are telling you and the feeling of disorientation and nausea should quickly fade away.
Also, this may sound a bit daunting, since you suffer from air-sickness, but at the end of each flight get your instructor to pull some un-usual attitudes or g's on you (e.g. steep turns). This will de-sensitize you eventually. Be brave!
Be careful with taking anti-nausea medication, always consult and AME for advice before taking such medication.
A career in aviation is definitely not out of the question - this alone will not stop you!