I think a transformer is also faulty because one lamp was out, I replaced the lamp but it still didn't work.
I think you are very likely correct in diagnosis of this fault, even though there is some dispute over the terminology.
What should I do to get it all working?
*I would firstly. for the moment replace the dimmer with a standard rocker switch, then retry the circuit, if the circuit then trips again with can investigate further and conclude the dimmer switch has been affected and damaged by the trip.
*If the circuit does not trip, but the lamp that the switch was operating is out, then it would be wise to look at a the box that has transformer printed on it as faulty, you could test by use of a voltage indicator (two pole) to see if voltage is getting to the unit by testing at the primary supply side for 230V.
If voltage at this level (possible nearer 240V) is getting to the "transformer" then I would conclude that the transformer is faulty and the cause of the trip and requires replacing.
*If the circuit did continue to trip when replacing dimmer for rocker switch, I would prove the circuit is dead at the suspected transformer where lamp is not working and disconnect it from the circuit, re-energise and see if the fault has then cleared. If it does then we can conclude the "transformer" is faulty and causing the trip, so would require replacing with one suitable to deal with load and dimming.
The above applies to any lamp that is not working.
*If neither of the above resolve the issue then further investigation would be required to the hardwiring of the circuit or the lampholders at the fittings.