I assume that you aren't even considering folding?

I usually like a shove more when I have bottom or middle pair with my flushdraw, top pair is usually worse if your kicker is bad, like it is here.

With this preflop action you need to worry about 44/QT/QJ/KQ/FD. You are in pretty bad shape against 44 and QT and a slight underdog against QJ and KQ, but you are ahead of any flushdraw (except AcKc). If you think he will fold QJ/KQ, but call with a flushdraw, then a shove here is probably best.

It's perfectly fine to call here and check/fold the turn if you face a very big bet without improving (a check-raise on the turn is good if the next card is a J or A). You will often get to see the river for free.

People tend to overplay TP+FD sometimes.