Is there any way to increase hand size, more meat, bigger hands?

Techniques to Increase the size of one’s hands are incredibly limited. Anyone offering injections of any kind would be more interested in collecting your money than in actually offering much benefit. There are no reliable, safe and accepted methods of increasing all of the bone lengths which would be required, plus this would be a very time-consuming and difficult process for you  to undertake.  
The best option for muscle growth remains a dedicated exercise routine.  I strongly recommend obtaining a resisted squeezing device for this. You can find one online or at a fitness store.   the key will be to use it regularly and gradually increase the number of repetitions. Once it becomes easy, it will be time to get a device with greater resistance. Before too long, you should have much stronger hands with an improved muscular appearance and an improved grip strength.