Can I overuse my dry eye drops? 

Drops for dry eyes usually contain a lubricant and a surface conditioner. All eyedrops on the market these days are preservative free. They are generally used 2 to 3 times per day on a regular basis. If you are not using it on a regular basis then you are missing out on the conditioning. On days where it is dryer or you have been using the computer for example then it is generally acceptable to use more often.  
If , however you find that you are using the dry eye drops more and the dryness is increasing then it would be advisable to have a check up with your Optometrist to make sure that there are no other conditions that are leading to the dryness.