The walk from Terminal E to Terminal B in Boston is likely to take more than 7 minutes. You will also need to clear security in Terminal B. But I wouldn't worry about the schedule as long as it's all on one reservation. US flies hourly BOS-LGA and will just put you on the 1 PM flight if you miss your connection.

There is also a free shuttle bus (at most times of day) that circles around the airport without going to the T stop. In your case it would run E-A-B. If you take this, note that Terminal B has more than one stop, and be sure to get off at the US Shuttle stop.