Before you go to heavier strings, change technique, etc., set up the guitar if it isn't freshly set up right now.
This will establish a baseline to evaluate before make any changes. A proper setup will include setting the neck relief. If you have too much relief you will likely fret sharp, especially between the nut and the 4th or 5th fret.
If your used to having to push on the strings, adjust the action to be higher off the fretboard. It's not necessary to have low action, that's why there are setscrews so you can adjust it the way you want it
Whoa, hold up before you modify anything including string gauge. Just keep playing until that tele breaks you in and it will. Like the others said work on your grip. You don't want that to be feeling anything like your acoustic. You will grow on each other. Peace bro.