learning with finger injury

It is your choice, Its my personal belief that anybody can learn to play the guitar, no matter what unfortunate circumstances. I once saw a guy with no arms play a acoustic guitar with his feet and sing at the same time, and it was only inspiration and proof that humans are capable of anything they put their mind to.

Since you lost your left index finger, here is your situation:

On a right handed guitar, you pick with your right hand and fret with your left hand. There are alot of players that do not play with their pinky finger, and use only their index, middle, and ring to fret across notes. I imagine, with practice, you could accomplish that same, fluid movement with your remaining 3 fretting fingers, its all stretching and muscle memory.

However, on the other hand (no pun intended) if you were to learn a left handed guitar, you would be fretting with your right hand and picking with your left.

There is certainly no reason that I can think of that would disable you from picking with your left hand, especially considering the fact the only the tip of your finger is missing. This would give you the your whole right hand to play the neck.

Its really just what you think you'd be more comfortable with. Learning to play left handed would probably take more time, but might be the "economical" way of doing things. However, playing right handed is still perfect applicable. Hope I helped.

Sorry about your unfortunate injury. Since the fretting hand is the one that requires more subtle and precise finger positions and movements, it should be your non-injured hand. Your injured hand can probably handle the strumming/picking duties. Basically, this all means you should learn to play a right handed guitar.