... the circuit goes though 2 rooms and it would be difficult to make sure I have visually inspected each wire.
Is this circuit feeding sockets along the way? I.e. would you expect many joints and cable changes? If not then checking at the panel and at the end point should be enough.
If you can't reliably determine its rating, and you already have issues with the breaker tripping, it would be very unwise to simply increase the breaker rating. Ideally you should measure what the circuit load typically is and fix any problems with the lights, etc. That can be
very dangerous to attempt as you would be placing a clamp ammeter on the cables in the panel or wherever easily accessed while it is live. Really you ought to get a professional electrician in for that sort of thing as live work (panel open and energised) is potentially very dangerous, not just electric shock but also the risk of arc-flash injuries.
I found an article a couple of years back and it had stats for 2013 in the USA with:
- 30,000 Arc Flash Incidents per year
- 7,000 Burn Injuries per year
- 2,000 Hospitalisations per year
- 400 Fatalities per year
- 80% of Electrical Worker fatalities are due to burns, not shock
So you really need to treat things carefully.
If you do have a high load that is tripping the circuit, say the pump motor start-up surge, it might be better to add a dedicated circuit for that than to modify the existing one if you can be sure of the cable section throughout the circuit.