The two good options: Feats and Multiclassing
It is quite unrealistic that your party finds hundreds of Potions of Healing during adventureing. Even if they could, it is a huge waste of resources.
Healer: It was mentioned before, quite an obvious choice.
Inspiring Leader: Does not give you as much HP as Healer, but in many ways it is still better. If your Fighter with 30 HPs receives a blow with 32 damage, this one keeps him swinging, so contributing to the victory of the team. Healer only works the persont taking the feat is around, and can spare an action.
Magic Initiate: As name moniker said, one 1st level spell is not worth taking, and there are no healing cantrips.
Depending on your party composition, different options are the best. You can use any spell slot to cast a spell known from either of your classes. So a 3rd level Wizard/1st level Cleric can cast Healing Word in a 2nd level slot.
However, you should not forget the attribute requirements for multiclassing, both into and out of a class.
Bard: Often overlooked as healer, but it has better healing options than a Paladin.
Cleric: Great choice for a Wizard or Wild Sorcerer, best healing spells, Medium Armor (Life, Nature, Tempest and War even gives Heavy Armor).
Druid: As above, but the armor proficiencies are much worse. Two levels of Moon Druid can add a multitude of Wild Shapes, great for HP replacement. Especially good on a Monk, as they can use Unarmed Strikes while Wild Shaped.
Paladin: Surprisingly bad at healing, cannot cast spells until level 2, and does not gain Healing Word. Aura of Vitality is great, but you have to wait 9 levels for that.