The fitness of a service is decided by a load calculation
This is a calculation which tallies each load, allowing for certain load factors. Typically these calculations are done in VA, which is volts * amps (as you might guess).
For instance, all general receptacle loads are figured at 3 VA per square foot of the house. Kitchen and laundry room circuits count as 1500 VA each. Electric ranges have some fairly complicated math so they work out to less than you'd expect. A dryer is typically penciled in at 5500 VA (pretty close to accurate). And you ignore either the furnace or air conditioner, depending on which is lower.
The problem is, you have resistive electric heat
And you really need to talk to the electric company and see if they have a rate structure appropriate for someone like you.
Because generally there are only 2 reasons someone would install plain electric heat like this: a) the power company offers a favorable rate structure which encourages it... or b) the house builder was very, very cheap and made the house $1500 cheaper by choosing heating tech that would stick you with a $500/month electric bill.
To give you an idea just how cheap electric heat is to build... consider this Cadet 2000W / 6800 BTU/hr baseboard heater which sells for $58. It's not cheap like Chinese; it's a perfectly high quality unit that will run for 30 years. One #12 cable can power 2 of them. Zoned heat, no exhaust... it's beautiful. The problem is, it costs 25 cents an hour to run at normal energy prices... running 1/3 of the time, that's $60/month per unit, and you'd have 1-2 per room!
The other problem with electric heat is you use a LOT of it, and that is a big load on the panel.
Honestly, an "all-electric house" (dryer, range, water heater, A/C) without electric heating pretty much maxes out a 100A panel. With electric heating, forget about it!
You need to convert to either heat pump or gas
It may be time to get a propane tank and install a gas furnace.
One option is go with a whole-house heat pump, which doesn't "make heat the hard way", it steals the heat from outdoors. It's like an air conditioner in "reverse"; it makes your house warmer by making the outside colder. It's also an air conditioner in "forward" - heat pump systems also work as air conditioning systems. Two birds with one stone. Because it's only pumping heat, it uses a great deal less electricity. However, it does not work at all if the outside is too cold -- so you need something as a backup. Which is back to straight electric heaters.
So it's ironic, even though heat pumps don't require 200A service, the fact that they need heat-strip emergency heat means you need 200A service after all.
A friend of mine lives in a truly all electric house: Water heater, range, dryer and a heat pump system. It takes a 400 amp service because the emergency heat is 140 amps all by itself.