Is it okay to use training data for validifying the trained model?
Scoring your model using the training data is not a best practice.  The reason is that you have already used this data to develop the "guess" at an accurate model.

This is akin to saying - 'Pick a random number between 1 and 10 (20 times)', here's a list of the last 10 numbers I picked to get you started.  You pick 20 new numbers and come up with 5 correct (25%).  What you are suggesting is that instead of reporting the 25% accuracy, that you would throw the first 10 back into the mix and report a 50% accuracy because now you've gotten 15 out of 30 right.

So there are two different things here.  The MSE of your initial model against the data you gave it - provides you and understanding of how well the model demonstrates history.  While the MSE (or other error metric) of the 'test' data shows how well you can predict the future.