Does a Melee Spell Attack use your spellcasting modifier in addition to be proficient?

Melee = sets the range (within your reach)

Spell Attack = spellcasting modifier + proficiency

1st level Druid casting Thorn Whip (with a 16 Wisdom) = 3 (Wis Bonus) + 2 (Proficiency), correct?

Yes.

Here's the relevant text from the 2024 PHB Spells chapter (it's also in 2014, probably the same place)

Attack Rolls

Some spells require the caster to make an attack roll to determine whether the spell hits a target. Here’s how to calculate the attack modifier for your spells:

Spell attack modifier = your spellcasting ability modifier + your Proficiency Bonus