The Balance of Adding Dice to Damage
Adding dice to damage has three effects:
- Adding at least 1 damage (already competitive with a +1 Arrow)
- Adding up to the dice's maximum in damage (far better than a +3 arrow at endgame when misses rarely happen)
- Doubling these effects on a critical.
As you can see, adding an elemental damage die is generally better overall than having +2 or +3 Arrows, even adding as few as 1d4 damage to the dice.
The reason spells like Elemental Weapon and Flaming Arrows can do this is that they occupy Concentration and use up a 3rd-Level resource. You can generally consider a 3rd-level spell to be a source of about 8d6 damage to multiple targets (Fireball benchmark), so any use of this resource doing about this much in certain situations is balanced.
1d6 per attack in a three-round combat is roughly 9d6 additional damage for an 11th level Archer Fighter, which edges out ahead of Fireball in terms of single target. It lasts an hour, which can be multiple combats.
An at-level casting would be 2d4 per attack in a three-round combat is roughly 18d4 additional damage for an 11th level Archer Fighter, which is about 50% more damage than Flaming Arrow at that level for a 5th-level slot.
An at 3rd casting would be 1d4 per attack in a three-round combat is 9d4 which is about 8d6, which is just a single damage short on average from the Fireball Benchmark.
Both of the above use costly resources and occupy the concentration slot of at least one caster in the party. An bundle of arrows that adds dice without spending resources of this level should be valued at the potential utility of those resources.
This can get really expensive and not worth the trouble. However, if I were to price it, I'd say 20 arrows for the cost of a 3rd-Level Spell Scroll (this is a pricing which depends on a setting-specific economy).
The Alternative: Changing the damage type
Changing the damage type does not affect damage distributions of weapons except against targets with resistances and vulnerabilities to it. This is inherently easy to balance because it has no major impact on targets without resistances or vulnerabilities to that type. You simply need to use the gold cost of changing the damage type to limit how advantageous future encounters are for the archer.
Silvered Ammunition from the Player's Handbook (which does exactly this for Silver resistance/immunities) costs about 100gp per 10 arrows.
You can silver ten pieces of ammunition for 100 gp. This cost represents not only the price of the silver, but the time and expertise needed to add silver to the ammunition without making it less effective.
Player's Handbook, page 148
Addressing your worries
If you choose to go about the changing the arrows damage type without affecting damage, they're a pretty on-par option with Silvering Ammunition which is balanced.
If you choose to go about adding elemental damage to arrows, you need to make sure that it costs about as much money as it would to get a single cast of one of the mentioned spells on you for a combat or two, which can be balanced if priced appropriately in a campaign where wealth is being distributed reasonably.
Balancing by limited supply is a bit much unless their effect is massive. If they're rare and the impact of the arrows isn't bombastic, players may end up just ignoring them. If they're common and cheap, your players may stock up on way more than you want them to have.
Using the pricing for Silvered Ammunition and noting that it requires a skilled craftsman who knows how to make them is a good enough limiter on arrows of the damage type variety. Using the pricing for arrows with added elemental damage, the price is already the limiting factor, no matter how common they are.