Any health professional can run a B12 test, and in people with Crohn's this test should be a standard procedure, just like the CRP and ESR tests. There's no need to wait for a specialist. However, you might want to find a family doctor who is more willing to run a simple B12 test.
Especially in cases of burning hands, one of the potential signs of nerve damage, B12 should be considered. Some of this damage might be irreversible. If you really are that deficient in B12, then it can be affecting your entire body, including your brain. This happens to be a critical vitamin.
I'd get that blood test today. Then I'd ask to have the B12 shot administered right after the test, rather than wait for a week to get the results - time, potentially, for more damage to be done.
B12 is perhaps the safest vitamin to take, so the shot shouldn't do any harm, and it is the best way to get B12 into your system, fast. Even people who don't have Crohn's are able to absorb only a small percentage of B12 vitamins.
Btw, IF the blood test is done, then any result below 400 should be considered as a sign you might be deficient.