Turn the heaters DOWN!

All space heaters are 1500w on high. That is 12.5 amps. However, most have a "LOW" setting that is 700-800 watts, or 6-7 amps.

See how to get "under 20" out of that? Just use "Low"! (remember you have to account for everything else on the circuit too).

My winter cottage has a 30A/120A main breaker and two 20A branch breakers. That's right, the whole house. We use space heaters a little, and as you can guess, we run ONE on high or TWO on low. My sweetie isn't me, and yet, we have this down pat. I start to make toast, sweetie kicks the space heater to "low". Apparently we know what we're doing, because we've had 3 breaker trips in 15 years here.

Breakers protect wires in the walls from fire

They already used the largest breaker that is safe. (assuming the wiring is yellow Romex; if it's white then they already oversized the breaker).

Installing a larger breaker is the same thing as installing NO breaker! (that is a thing, it's called a "Subfeed Lug Kit"). If you want to do that, that's between you and your insurance company LOL.

Upgrade your installed HVAC

First, you shouldn't be using space heaters as primary heating. If your additions's main (built-in) heating is inadequate, upgrade it. If you didn't spec any and your plan all along was to use plug-in space heaters, that's a waste of money. (I bet you thought I was going to say something else lol). Seriously, because of the cost of those space heater! (I bet you thought I was going to say "electricity" but that too). It's also unbelievably unsafe, and insurance won't pay because the machine's instructions specifically say not to run it unattended.

If your addition needs more HVAC, let me clue you into the latest cool thing: The "Mini-Split Heat Pump. Does both heat and cooling and takes a tiny amount of electricity for the heating (and cooling) it does. It's 200-600% more efficient than electric heaters. And you get "free" (well very cheap) A/C as part of the deal. Goodbye loud window units or dreadfully inefficient portables.

If that's too much for you, and you'd rather have electric heat, then since you're installing new circuits anyway, install baseboard heaters. For instance a 2000W Cadet heater is around $60 and is safe and legal to run unattended. It will also last 40 years, unlike those rinkydink space heaters that don't even last a season.

You can run a 2000W and 1750W Cadet heater on a single 20A circuit run with 12/2 cable - the very same stuff you're already planning to add to solve your problem. And now you have proper heaters - it can have an external thermostat so it's more reliable, it can even use "smart stats" like the Nest (though 24V thermostats will require addition of an "Aube style" relay).

However Cadets are just as costly to run as space heaters (in electricity)... and in a couple of seasons a mini-split will pay for itself in lower heating bills and be cheaper to run as A/C also.

The wiring was legal as done

I actually used a "professional". He's the one that was supposed to run separate wires and breakers for each room. He cut corners and just ran them all together. I had the space in the panel box and I bought 4 breakers so that he could do that. He only used 2 of the breakers...one for the laundry room and one for the hall, bathroom and bedroom and outside outlets.

That's exactly the Code minimum. The laundry room must have one circuit that is dedicated. All the other rooms are allowed to be on the same circuit per NEC. However, NEC is a slumlord "bare minimum" beneath which the house is unfit for human habitation. You can aim higher.

If your guy failed to provide the contractually required circuits then you need to go back and demand that. If it was verbal then that's not worth the paper it's written on. Setting your house on fire is not an appropriate response to contractor underperformance. It's also possible the guy is not a licensed electrician, and if so, they may have violated the law doing the work. I would have a talk with the inspector about that.

It's also possible your contractor brought in a sub who is a licensed electrician, and failed to pass on your written requirements, in which case that's between those two people and you're owed correct work.

If it were me, I would first ask - maybe they ran three separate home-runs and simply merged them onto the same breaker because you didn't have enough breaker spaces. If they ran a single home-run, I would segment that into 3 sections. Where sections 2 and 3 meet (2 choices of junction box here), I would run two 12/2 cables back to the panel (the cost is in the fishing; tossing in an extra cable costs very little). They'd feed sections 2 and 3, with section 2 being fed "from the wrong end" but that's fine.