Can I make my cellphone a 3.5mm jack bluetooth transceiver?
No, what you want cannot be done, at least not in such a simple way.

You could use a cable that converts the TV's signal to a signal that the microphone input of your phone could use. But then you'd still need some software to take that signal and make a Bluetooth stream from it. And even if you managed that it would be a mono (not stereo) signal as the microphone inputs on phones are generally mono only.

Recommending devices is off-topic actually but I'll humor you since I know exactly what you need:

What you can do is buy the same device which I bought recently:

 

Here's an ebay link

This can be powered from a USB charger and converts 3.5mm jack analog audio to a bluetooth stream.