Is a 13 year old fat if they weigh 135 and are 5 foot 3?

It's marginal.

An adult who is 5' 3" is at a healthy weight between roughly 113 and 141lbs.

A teenage girl is likely just going through, or has just gone through, her major teenage growth spurt.

So you'd expect her to be towards the lower end of that scale (say 113 to 130lbs)

A teen boy is likely not yet reached his major growth spurt, and so might be anywhere in that range.

So, don't fret about it if you are 5'3" and 135lbs.

But it's worthwhile taking a sensible healthy approach to eating, and a making sure you get some physical activity every day.

If any of the bodyweight is excess fat, you'll be able to use it up as fuel over the next few months without too much effort.