My mom gets pterygium, so am I likely to get it later?

Possibly yes. Pterygium:very common, abnormal growth of clear covering (conjunctiva) of white part of the eye (sclera) over the cornea (window of the eye). If severe and causing discomfort or red, it can be removed with surgery. It is generally benign. It is due to excess sun/UV, genetics plays role. Prevention is only remedy. Avoid sun (sunglasses, hat); avoid smoking. More info: eyedoc2020.blogspot.c.
Possibly. Pterygium, a non-malignant growth next to the cornea, has a modest hereditary component. If you are exposed to the same environmental influences -sunlight, dust, wind - you probably have a slightly higher risk than the average. Since this is mostly benign, and can be treated, do not worry about it. You will see it in the mirror if it happens.
Family history. Family history does seem to increase your risk but the biggest factors are sun exposure, location close to equator, race.