What you are experiencing could be what I would call an overuse injury caused by repetitive stress to muscles, tendons and joints without adequate rest for recovery.
Many athletes experience this type of injury and it is often exacerbated by using improper form. But even if using proper form, continual stress without adequate recovery time can lead to a repetitive stress/over use injury.
I have seen these type injuries occur with experienced professional guitarist who book too many gigs in a short period of time and they end up with a similar issue. Even though they may have been playing regularly for many years without injury. It's when they over do it without adequate recovery time and rest between gigs that the injuries show up.
Your best bet is to rest for an extended period. Similar to when the doctor orders bed rest, you may need to lay off any unnecessary use of your hands for as long as a few weeks (or more) to allow for full recovery. As disconcerting as this may sound, this means no drumming either. While playing drums stresses different muscles, joints and tendons than playing guitar, there will be some overlap.
When you resume playing, always start with at least ten minutes of warm up and stretching exercises. Try to avoid playing more than one hour at a time without a ten minute break and try not to play any more than 4 hours a day total. It's best if you can space out your practice sessions throughout the day. Say an hour in the morning, an hour at lunch and an hour in the evening instead of 3 hours in the morning.
Here is an article about the importance of warming up prior to playing guitar including some suggested "exercises". Guitar World Article on Warm Up Routine
Here is a good YouTube video that shows how to do some stretching exercises for guitarist. YouTube Video showing stretching routine
I know it's hard to stay away from your instrument, but trust me, it is best to allow your body (hands) to fully recover before resuming. Otherwise you start chipping away at an "open wound" so to speak - and will likely end up right back where you are now.
I wish you the best.