I had a 2nd degree burn from hot coffee spilling on my hand almost 2 months ago. the burn now looks light pink/sometimes very pale. will this go away?

Soften with time: Yes it will likely lighten with time" avoiding sun and tobacco use is also important as well as topical silicone gel sheeting or ointment.

Possibly: Burns always improve with time. Color changes occur over several months. Depending on the depth of the burn, normal color and appearance can occur.

Sounds like a scar: The color will change over time sometimes even day to day. It tends to progress to a more normal color over months to years if you have pigmented skin the scar is may remain pink or pale much longer.