Previously I had blood in spit for a month doc gave anti biotics now I dun see blood. Does that mean the anti biotics worked, ? Doc says it must be.

Find the real reason. Antibiotics are for infection. Period. Some have other indications but, in the absence of known infection, they should be avoided. You need to find out why you had blood in your saliva/sputum. This can be serious so, you should see your im physician immediately. If your doctor is giving you antibiotics for no reason, consider switching...
Probably. If you were coughing up blood you need a chest x-ray. If one was previously performed and was ok then no further evaluation is needed at this time, but if you have not had a chest x-ray, one should be obtained, with a history of coughing up blood.
Needs follow up. Blood in sputum could mean more than one thing. It will need a follow up, not only of that sign, but also if there is fever, night sweats, weight loss, persistent cough or complete resolution. If there are other concerns your doctor will most likely need to do do further testing.