You should definitely see another neurologist if you're unhappy with your treatment but it doesn't sound like you have anything to worry about. You have two jobs, one of which is hard labor? That seems fairly likely to cause muscular tension that could easily cause headaches. From your description, it doesn't sound like you're too horribly affected by the pain (I think you said so at least...), having 3 second shots of pain every 2-3 hours, adding up to about 30 seconds of head pain a day? I totally understand why this would worry you, but if it isn't having a significant negative effect on your life then it's very unlike to be anything that you need to concern yourself with unless that changes. You may have had a bad doctor but it's equally likely that he concluded that there's no indication that anything worrisome is happening to your body other than the pain that you say isn't a problem.
Personally, I have had headaches for 5½ year, but with severe pain every second of every day. I've had incredibly extensive testing and we haven't found anything else wrong with me--if I weren't in horrible pain constantly (with some nausea, etc) that I contrastingly find unbearable then there would be absolutely no reason that any doctor wouldn't do some simple tests and send me on my way. It seems like the doctor probably reacted appropriately in accord with your level of complaint. It's not common for any doctor to request any more advanced testing than you received without more troubling symptoms. No ethical and intelligent doctor would order advanced and expensive testing unless a patient were having significantly bothersome symptoms or if the doctor had any reason to think that you are at any significant risk of developing such symptoms in the future. It's also very unlikely that any insurance provider would agree to pay for more advanced testing if it seemed unnecessary.
But, again, it is absolutely your decision if you feel concerned enough to see another doctor. Two doctors' evaluations are more reliable than one, but don't necessarily expect to have extensive testing ordered.
One thing you may want to consider though: if you agree that there's a chance that you have a problem with muscular tension or other physical or mental stress then you may want to consider seeing a specially trained psychologist that can train you in biofeedback or other relaxation techniques. Any of these things would help reduce these potential problems (and possibly reduce your bursts of pain directly). Biofeedback is especially useful as you learn to effectively relax your entire body while being connected to simple monitoring to measure your muscle tension and other factors and train you to be able to mentally reduce them, provided that you put regular effort into practicing. To me, that seems like the direction that I would look if I were in your place.
I hope that you continue to be healthy!
DX: NDPH, Recovered CRPS
RX: Lamictal, Provigil, Clonazepam, Ambien CR, Emsam, Namenda, Oxycontin, Oxycodone
PRN: Haloperidol, Zyprexa, Lodine, Zofran, Skelaxin