1. No, you will not get an MD at the end of Internal Medicine residency, no matter where you do it - as hypomanic pointed out, your MBBS is viewed as equivalent education to an MD and qualifies you to complete a residency, so long as you pass your USMLE steps and achieve ECFMG certification. The MD is an "undergraduate" degree in the US only in that it must be completed before postgraduate medical training (i.e. residency and fellowship) - US MD's must have undergraduate (bachelor's) degrees before entering medical school.
2. You would be at a distinct disadvantage applying for an infectious disease fellowship without US residency training - I'm not even sure you would be considered.
So - I think it would definitely be in your best interest, if you want to train in infectious disease in the US, to secure a residency in the US. Hope that helps.
Edited to add: Postgraduate medical training does not require tuition; indeed, you will be paid a stipend in residency and fellowship.