Can stars come in non-round shapes too?

They certainly can! There are several ways this can happen. First, is that they can be rotation so fast that their polar diameter becomes smaller than their equatorial diameter. The planet Jupiter rotates once every 9 hours or so, and its shape shows this rotational flattening effect. Stars don't really get very flat by this process because very few stars spin faster than 100 km/sec at the equator and this isn't enough to really flatten them very much.

The second way that stars can become non-round is if they are in a binary star system so that the gravitational pull of a nearby companion star distorts them. Stars that orbit each other with about the separation of the sun from mercury get noticeably 'ellipsoidal', and many of the so-called 'compact' binary systems have orbit periods less than a few days! This means that their outer atmospheres are nearly in contact, and so the gravitational forces pulling on the stellar gases is enormous. To imagine what these stars look like, imagine two footballs nearly touching each other along their long axis!Binary stars can continue to orbit like this for thousands of years before tidal 'friction' causes the orbits to decay and the stars to merge into one single star.