Scar/lump on both sides of alar base. Is this normal? (Photo)

It is very early to ultimately tell but it appears that the alar incision was made slightly above the groove and the remnant alka is the bump you are concerned with?  Its likely this will continue to improve with time however its best to discuss this with your plastic surgeon.

Each person recovers differently from Asian rhinoplasty. Subtle changes and definition of the nose continue to develop for several months post-op as the nose heals and settles, and it can take up to 1 year to achieve complete healing. At this point, only your surgeon knows your history and can advise you whether steroid injections are recommendable. You should consult her/him if you are still concerned.See attached links for more information. 

Hi Christyli,

Since it is only 8 days (as of taking photo) post-op, it is hard to evaluate the scar, but normally, scars improve as the incision site settles. Pleease wait at least 3-6 months for the area to settle. At this point, you should not do anything to the surgical site anyway.