You should have a minimum of two 20 Amp circuits, GFCI protected, for counter-accessible convenience receptacles. Lighting and installed appliances may not use these circuits, nor may receptacles in other rooms.
The bathroom should also be on its own circuit, with GFCI protection for the receptacle(s).
How did you "upgrade" the amperage without running new circuits? The maximum allowable amperage on each circuit was probably already reached for the existing wiring with the fuses.

Thanks for the reply Randy. Im not sure how it was upgraded but i was told it was when the service was upgraded and moved and the panel added instead of the fuses. The old circuits were definitely overloaded. It looks like the dishwasher, gfi for bathroom and kitchen, and boiler are all on their own switches along with a couple other new things...

I just switched off that one that tripped the other day and this is what is on it: 2 basement lights, kitchen light, 1 kitchen plug(non gfi), washer/dryer outlet, other outlet in same room, upstairs hall light, 2 bedrooms minus one new plug, and a porch light.

Any idea what i should say to the electrician when i call him to come fix this? and should i have to pay for it?

You are not required to have an arrangement that meets the current electrical code unless you are doing a significant renovation to that particular area. Just guessing from your description of the previous service, one fuse except the boiler, your house has not been worked on significantly in may years. How many fuses were in the fuse panel that was recently removed? How many active circuit breakers do you have now? Is the refrigerator on a separate circuit now?

Since you are tripping breakers, you need more circuits. It is that simple. With the service entrance upgrade you probably got a new circuit to the dishwasher. It is hard to say what else.

Who should pay for further updates? I don't know what the deal was with the electrician. If what was agreed to was installed, the deal is done. That said, what was the discussion like when making the arrangements? If you were not, I don't understand why you were not encouraged to have two circuits in the kitchen for wall outlets in addition to the DW and refrig, another for each bathroom and another for the laundry. Splitting out lights, and receptacles in other rooms from existing circuits might be too much expense for what it is worth.

Of course you should pay for it.

Initially the electrician did what he was hired to do I assume. And I assume this was not to re-wire the whole house but do a service upgrade and add a few circuits.
It would seem to me you had him add circuits but missed a few places that needed them, like the kitchen counter.

A service upgrade will NOT separate the existing circuitry in the house.

good, thats what i was hoping someone would say. thank you.