The beginning of statement A is in the Past Simple “I just checked” whereas the beginning of statement B is in the Past Continuous “I was checking”.
The Past Simple tense is used to talk about an action that happened in the past and finished in the past. For example:
- I was asleep, now I am awake.
- They went to school yesterday.
- He played a match this morning.
- We worked 45 hours last week.
As you can see from the examples above all the actions occurred in the past and were completed in the past. The Past Continuous (or The Past Progressive) tense is used to talk about an action that was in progress at a specific time in the past. For example:
- I was sleeping when the doorbell rang and woke me up.
- They were going to school yesterday and met their friends on the way there.
- He was playing a match this morning but stopped when is started to rain.
- We were working 45 hours last week to reach the deadline.
As you can see, the Past Continuous allows us to talk about two actions in the past; an action occurring or in progress in the past and a completed action in the past.
Statement A begins the Past Simple but ends with the Present Simple tense, this is because the action of occurred and finished in the past and we are now talking about present time (I go out).
Whereas the beginning of statement B is progressing in the past (I was checking) while another event is completed in the past (I went out).
Yes both statements can be used to answer the question “What were you doing here?”