I share your pain (both literally and metaphorically). I'm also a software engineering and I also play the guitar. Only last month I injured my left hand and I had to take a break for 1 week, then play softly for 1-2 weeks until I regained my full strength.
To answer your question:
Can I injure my hands by typing or playing guitar too much?
Yes, you can. It is within the realm of the possible.
The way to minimize the chance of this happen is to improve your posture and technique. Perhaps the computing side of the answer falls outside of the remit of music.se; there's plenty of advice on the Internet: use an ergonomic chair, use ergonomic keyboard/mouse.
When it comes to guitar, try to work on your technique. Musical technique has developed over the centuries for a reason: it reduces the chance of you hurting yourself.
Things that have worked for me:
I start my practice with some warm-up exercises including scales and "the spider". They are boring and it feels like a drag, but I my fingers feel different after a few minutes of this
I occasionally do some finger stretches (like the ones described here)
When I play sitting down, I rest my guitar between my legs, and use a footrest on my left leg. This is the classical guitar position. Looks a bit strange for acoustic/electric, but nobody's watching when you practice, right? The reason for this is that if I rest the gutar on my right leg, my right elbow pushes the body of the guitar into my body, causing the fretboard to pivot away from it. This means that I have to stretch my left arm to reach the fretboard, causing more tension on my forearm and the tendons on the back of my hand.
I'm using lighter gauge strings (used to use .10's, now went down to .9's). I noticed pain when I was doing some bends and this makes it much easier to bend strings.
I'm improving the technique of my bends. In particular, Santana-style unison bends (bending the 2nd string with my ring finger 1 tone up while at the same time hitting the same note with my index) were hurting a lot. I practice them slowly and use them sparingly. Will use them more when I have improved the technique.
I'm changing the technique with which I play barre chords. Instead of keeping my thumb vertical, I'm moving it 45degrees along the back of the neck. This seems to cause less tension on the muscle between thumb and index finger.
In general my advise would be to play slowly and listen for any indication of tension in your fingers/hands/wrist/arms/back, and find a technique that reduces that.
Good luck and stay healthy!