I am 18 and i weigh 51 kgs.is it possible that i could grow an inch taller within a year or so?

Probably no: Insufficient information, what's your current height? Your given weight is bit in the lower limit, your overall health and maturity need to be evaluated, you may add some more weight but not height unfortunately, check this link for girls growth chart, good luck http://www.cdc.gov/growthcharts/data/set2clinical/cj41c072.pdf

Maybe: Your potential for more height depends on the activity of growth centers in the bones. Most females who enter puberty at the average time close these centers by 16-17 or 7.5 cm after first menses, ending the process. An x-ray of your wrist/hand might show you have open growth centers.If you started puberty late, this would be more likely. Chances are, you are as tall as you will ever be.