Right breast has not dropped like left one. Is it because I'm right handed?

At 1 month after surgery it is common for the implants still to be dropping at different rates.  In the end, it is usually not a problem, but can sometimes take 6 months.  It probably does not have to do with handedness.

Despite having the the same operation for either breast the tissues respond differently. The tissues relax at a different rate and swelling dissipates at a different rate. I would continue to follow your plastic surgeon's advice and reevaluate your results three months from your surgery date.

There may be several reasons the right one is not dropping as fast. It is possible that you muscle is still keeping it up, another reason may be that the pocket is not fully developed on the bottom. You could also be getting a capsular contracture.  You should see your surgeon to be evaluated, but the most likely reason is that they just need more time to even out.

Breast do drop at different rates and many attribute it to the dominant side of your body, but there really isn't any way to know for sure. If one breast was looser than the other, this side tends to drop sooner. Continue following your doctors orders. I have seen breast change for up to 6 months after the surgery.

It’s
very normal to notice asymmetry in the breasts during the early stages of
recovery after breast augmentation, and one month after surgery falls into that
category. In right-handed women, the pectorals on the right side of the chest
tend to be stronger and more well-developed. This can mean that it takes longer
for the muscles and tissues surrounding the right implant to soften and allow
settling. The less-used muscles on the left aren’t as resistant, although this
effect is reversed in left-handed women. You’re still several weeks away from
your final results, so continue wearing your compression band and practicing
your massage and you should see your breast symmetry improve as healing
progresses.

Many people like to think that hand dominance has something to do with asymmetry after breast surgery, but I don't think it does, and I don't think there is any way to prove that one way or the other.  It is more likely that there was, or is, a difference in the breasts themselves, and that is responsible for the early differences that you are seeing.  The fact that your surgeon put a larger implant on that side makes me think a few things.  First, that breast might have been smaller, and thus slightly higher than the other, so this may result in the implant sitting higher early on.  Second, if your saline implants are the same volume implant but filled to different volumes, the fuller implant may project more or be fuller in appearance, and sometimes this gives the impression that the breast is "higher" because of the fuller upper pole.  In any event, it is still very early at this stage, and things will very likely change as tissues loosen and your implants settle.  Stay in communication with your  surgeon about your concerns and listen to his explanations and advice. 

Each implant may relax into the pockets at different rates.  THis can take 4 months and sometimes longer. Preop photos would be helpful.  

The time it would take for breasts to drop and achieve symmetry after an implant varies. For some patients, it would be faster. For others, it would take several months. It would depend on many factors such as the placement of the implants in relation to your muscles. Your handedness may affect the pectoral muscle, but only to a slight extent, and may not be the reason for the asymmetry.

Being right handed should not be a concern with your healing.  Breast do drop at different rates.  Follow up with your surgeon for an exam, and to discuss your recovery.  Best wishes!