I have had this problem, but in my case it ended up being a grounding issue. I am not sure that is the case with you though.
We know a few things, and that there was not an issue with your place until there was a storm in the area. Since power trucks were on your road, we can also conclude that there was damage done on your road. Now why your neighbor was not affected, and you were, could take the shape of many things. Some of it depends on whether the area lines are 3 phase or single phase, but also where the circuit breaker/breakers is for the main power line for your street.
There are a few possible results here:
1. The storm did damage directly to the circuit/circuits in question
2. When the power came back on it did damage to the circuit/circuits in question
3. There was damage done to the grounding of the electrical system somewhere on the home
4. The fuse box itself is damaged
By the way I read and reread your post, it seems the two fuses that keep blowing, are feeding a single 220 volt circuit. Is that correct?
1. To blow a fuse repeatedly means there is too much amperage in the circuit somewhere. That could take on the form of
water getting in on the wiring somehow, so it may be subtle, or in an area where you cannot see the wires. You said you had a storm, but what was it like? High winds only or high winds with heavy rain?
2. You have fuses which tells me the entire wiring system is rather old. Copper gets really brittle as it ages, so it is possible that when the power was returned by the power company, the sudden amp draw did damage to that particular circuit.
3. This scenario ties in with number two, but I have seen some really
goofy grounding methods in my life. If someone tied the neutral to the ground somewhere, and that is most likely the case with older wiring, goofy things can happen.
4. Again, either when the storm hit, or afterwards when the power came back on, damage was done to the fuse box, again a rather old electrical component.
Just because power did not go out in your neighbor's house, does not mean it did not go out in yours. I had a high wind storm one year pull the wires right out of my meter box. I was without power for 9 days, whereas my neighbors had theirs on the whole time. It also broke the components inside the meter box.
You could call your power company and find out what occurred on your street. I am not sure that it would matter because I think you are going to need an electrician. All it takes is brittle copper to break a connection somewhere and it will overenergize the circuit and cause it to blow the fuses. That is hard to diagnose online.