Pulling sensation in left breast - Should I see a doctor immediately or see whether it goes away?

You may be developing a capsule, but can see a plastic surgeon when you can get an appointment. This does not sound urgent.

From your question, it sounds like you've only been experiencing this pulling sensation for a brief time period, because of that I think that there is no emergency here. I don't think you need to get in to see a plastic surgeon urgently. It could wait for a week or more to see if it goes away on its own. Alternatively, you might call a plastic surgeon now to get an appointment scheduled in a non-urgent fashion. If it gets better you can always call and cancel your appointment or go in to get evaluated anyway for reassurance. If it was possible you might be best served by seeing the plastic surgeon who placed your implants.
As to what this could be it's possible it's of no real significance. Normal menstrual cycle hormonal fluctuations cause many patients to have breast sensitivity. Although I have no real experience with IVF, I would suspect it would be even more likely to cause changes in breast sensitivity.
As for breast implant associated causes, it's possible that your pulling sensation might be an early sign of developing capsular contracture. It is way too soon to seriously suspect that diagnosis if you've only been experiencing these symptoms for a few weeks. Since your breast implants are 14 years old it would be a good idea for you to be seen in person by your local plastic surgeon, preferably the one who placed your implants. If your implants happen to be silicone, it's probably time to consider imaging, high resolution ultrasound or MRI, to check implant integrity.
Hope this helps, good luck with IVF.

Dear ilz777,
I understand your concern. However, without a proper assessment, it would be difficult to determine what went wrong. It is best that you visit your plastic surgeon for further assessment or ask for a second opinion. Only after a thorough examination, you can get proper recommendations and advice.
Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery