Hi Vidisha, 

The pET22 b(+) vector lacks lacZ alpha peptide, so it can not be used for blue/white selection. You can use pETBLUE system to use blue/white selection.

You can screen your clones in pET22b vector through epilyse test where you can check the shift in size of your clone plasmid with control non-transformed pET22b vector in agarose gel. You can also double digest your clone plamid to get the insert fall off and later it could be validated by sequencing. Colony PCR is another way of detection of your clones if you have the primers but it's not always accurate. 

Hope it will help you.

Thank you gaurav