Drum Distortion

[Greykitkat36]

My band recorded a pratice session on my tascam 424mkIII. We mic'd the drums with one mic overhead. Everything came out well except for my snare. Whenever you hear the snare on the recording it comes out either muddy or distorted, and does not sound like a snare should. Any help on what I could do to fix this?
(Drums were Directly recorded)

 

[Drummer4Life05]

Mic your snare with its own mic.

 

[Greykitkat36]

I wish I could do that, but I dont have the budget. I only have 4 good mics. So, when recording with the band, I have to use 1 mic overhead. So, in order to fix the problem, should I maybe place the mic in a better spot? Because I had it in front of the kit overhead. Or maybe can I fix it in mixing?