Is it generally aloud to wear those long sleeve swim pieces in a public pool?

I don't see why anyone would have a problem with it. Most people would be far more concerned about someone wearing too small of a swimsuit in a public setting.

I have a few of those long sleeve swim/surf shirts and always wear them in pools, never had a problem. I'm just an overweight middle age white guy and I want to swim with my kids and get some exercise but I realize that seeing me topless isn't exactly most people's idea of a good time and its probably better for everyone that I wear a shirt.

I assume you're a trans man as I am, and don't want to be outed as having a mastectomy so simply showing them and getting over insecurity isn't an option. There's no reason those swim tops wouldn't be allowed in pools. You might get hot and people may look at you funny for a split second but no one will question you. If your scar is only on your chest though why do you need long sleeves? It's much more comfortable to wear an Underworks swimming tank or tee for me.

usually it is ok            .

Most people won't care about your scar. Having a scar isn't shameful.

But if you don't want it seen, there's swimwear that's high in front and covers the chest. You don't need to go to the lengths of a rash guard. (Although my pasty skin makes them a good idea for sun protection.)

Here's a whole page of high-neck swimsuits: https://www.landsend.com/search/S-xea?initialSearc... Some are one piece, some are tankini top and bottom.

Look for something similar.

I encourage you to let the scar be seen. Most people will quickly accept it and you need to feel the freedom of not hiding it. Hiding it does you no good and keeps you feeling insecure in the pool.