I've been taking guitar lessons for about two months and have seen a bit of improvement. I've been doing what the teacher has been telling me to do. Is there anything I could do on my own to improve? Like try playing my own songs or anything like that? Comments please, thanks!

You can always find easy songs to play on your own and practice as much as possible. I have always heard easy songs considered to have only 3-4 chords, as in G, C, D, & Em for example.