In Electrum under History tab if I right click on the unconfirmed transaction there is a pulldown menu with an option "Child pays for parent". Then I can set the desired Tx fee. Will this help?
Yes, it will be helpful. Just send the unconfirmed output to another address with a high fee.
Note that the fee should be that high, so miners include both transactions in a single block.
Assuming the unconfirmed transaction is A and the transaction you are going to make is B, the fee (sat/byte) you need to pay for transaction B will be as follows.
fB = (f*(SA+SB) - fA*SA) / (SB)
f is the fee (sat/byte) needed to be paid for a transaction to be included within certain number of blocks.
fA is the fee (sat/byte) has been paid for transaction A
SA is the size (byte) of transaction A
SB is the size (byte) of transaction B