My 3 month old daughter is doing just about the same thing right now...mostly when she tries sucking her thumb.
At night, I tuck a blanket in all around her bassinet matress below her armpits and tuck her arms underneath it so she cant get to her face. She hates having her hands covered,and moves her arms ALL the time, but this helps, if your baby cant or wont wear mittens (or socks as suggested) over her hands.
Good Luck!