How to resolve lifelink with multiple blockers?

No, you get life equal to the total damage dealt. Your creature has 10 power, so it will deal 10 damage in total and you'll gain 10 life. The way that damage is split up between multiple blocking creatures doesn't matter.

Cadence has already answered this question. The relevant rules are:

702.15b. Damage dealt by a source with lifelink causes that source's controller, or its owner if it has no controller, to gain that much life (in addition to any other results that damage causes).

and:

510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocked creature to divide its combat damage. However, it can’t assign combat damage to a creature that’s blocking it unless, when combat damage assignments are complete, each creature that precedes that blocking creature in its order is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.