breaker tripping

Hello friends
Replaced a smaller window ac with a larger one altho both were still 110s. problem is that sometimes the ac will trip the breaker, it is in the bathroom window and the breaker supplies both bathrooms electricity. don't recall the other unit tripping the breaker. House is about 25 years old and the breaker is a "American" brand? have a tough time finding replacements. Do u think that the breaker is just old and should replace with same size or should replace with a larger breaker, currently is 20 amp.
In the fall i want to replace the whole breaker box with a updated version.

 

You could replace the breaker with a larger breaker, but be sure to increase both your life and fire insurance first. But I recommend a can of gas and a match as a cheaper alternative.

Your story is fairly simple. You increased the demand on the circuit above what it can supply. I don't think replacing the old 20-amp breaker with a new 20-amp breaker will help. And replacing it with a larger breaker is suicide (you probably inferred that already). One solution is to put the old A/C unit back, and save the new one until after you update your panel and run a new dedicated circuit. Alternatively, you could continue to use the new A/C if you are careful not to use anything else on the circuit while the A/C is on. Be sure to turn off the A/C before plugging anything else into that circuit.

Replacing the breaker box by itself won't solve this problem. You also need to run new circuits.