Deductions & credits

Yes, you do have an abundance of tax considerations here. Let's address these one at a time.

1. Since you are a resident alien, you do need to include all your worldwide income. In this case you will need to include income earned in India.
2. If you received a tax credit for the US income reported to India for the Feb-March period, you will not be able to claim an additional tax credit on your US taxes.
3. However, you may claim a tax credit for the taxes paid on your January income earned in India. I will explain the steps to claim the foreign tax credit at the end of this post.
4. In determining the conversion rate to use, there are a number of online currency converter apps available to use on your phone or computer.  My suggestion is to access several to get a consensus on the best rate to use. As far as the IRS, there is no official conversion rate source to use. They accept the rate that is used consistently so this is why I suggest to use several sources and reach a consensus on the most consistent rate available.

Here is how to claim a foreign tax credit for your taxes paid in India on your Indian income.

1. Open Turbo Tax
2. Go to federal>deductions and credits>estimate and other taxes paid
3. Foreign taxes >start
4. Start answering questions. Make sure you answer the question correctly about if this is the first year you are making the simplified  election
5. Answer the questions in the next screens until you reach a screen that talks about income type. This will be the general category of income. if you have more than one country, you will add that later.
6. Next screen is where you add the country your foreign income was earned in. 
7. Next screen will ask you what your source income earned in that country. Here you will allocate income earned while you were in that country.
8. You will continue answering questions until you get to a screen that says foreign taxes paid to XXXX.   

@p_r_s