What does 憋得通红 mean here? 老板生气了为了员工都总是在玩手机。 他指着我：你说说，看了什么？比我说话还有意思？

我脸憋得通红， 说： 。。。。

我觉得‘脸憋得通红’得意思就是： 'my face went red' or 'I blushed' 但是‘憋’的意思是‘choke, stifle, hold back'. 
‘我’ 发不发红呢？

到底这里的‘憋’是什么意思？
*憋 means 'to hold back'--  most commonly: 'holding breath' (憋氣) or 'holding back urine' (憋尿)

In the case of '脸憋得通红', '憋' should be short for 憋氣 (holding breath), (too upset to breath)

脸(face) 

憋(holding back)

得(to the point of)

通(completely)

红(red)

To translate this phrase literally would be  'face turns red from holding back' . 

If you want to be precise, you can write 'face turns red from holding breath'. but it is not good English.

I think the best way to translate this phrase is to interpret the reason of holding breath directly, and write: "face turns red from embarrassment" (having difficulty to breath due to embarrassment)

Similarly, if the reason for the redden face was 'anger' the translation should be "face turns red from anger"