Like Replace, I am puzzled by what you are asking. People don't become 'immune' to antibiotics, though yes, bacteria may become resistant to them.
Do you mean you have developed an allergy to amoxicillin? Different question.
ETA: In that case, no. It just means that amoxicillin will not likely help with this particular infection.
Sometimes a partial resistance can be overcome by a higher dosage of amoxicillin, or by coupling the amox with another drug called clavulanic acid (the brand name for this is Augmentin). We do this for ear infections a lot. But depending on what you have, it may just be better to switch to a different antibiotic that your bacteria have not yet developed resistance to, and, one hopes, get rid of it once and for all. (This, by the way, is why we don't like to overprescribe antibiotics and why it's so important to take all of the prescribed course--so you don't develop resistances.)
For future infections, amoxicillin may work or may not. They can do tests that will tell a particular bug's susceptibilities, though they don't always do them (it takes extra time and money to do cultures) and just prescribe what usually works. If you have the same kind of infection again, you might want to mention that the previous one was resistant to amox at the start, because it's also possible to be colonized with a bacteria that usually doesn't cause problems but sometimes gets out of control.
The resistance is nothing to do with your body, so there's nothing to 'recover' from except the infection. The resistance is all in the bacteria, not in you. ;-)