Please wait for someone smarted than me to chime in but here’s how I’d figure it.

You can probably look at your furnace, AC, range and dishwasher and find a current rating somewhere. You could add that up, plus 10%,, to see if their right (bet they are).

Guesses for breakers:
Furnace – 30 amp
Dishwasher – 20 amp
Range - 50 amp
Total house outlet breakers – 40 amp
Dryer – 30 amps

Total – 170 amps

As you noticed this is more that 100 amps without your dryer. That’s because hopefully all your appliances aren’t shorting out at once.

I would just add another 30 amp fuse and see. If the main trips often upgrade or buy a gas dryer. A 30 amp breaker is not that much. Chances are you won’t have everything on at once (especially the furnace and AC). Heck, I’d probably just hook into the furnace or range breaker. I have a smoke detector.

But probably to be on the up-and up you’d need more than 100 amp service.

Looks like there are punch out panels next to the main. Maybe you can place a breaker in there.