It's been six days since my cat started wearing a cone. It's been six days since my cat started wearing a cone.

Correct - You could also say "My cat started wearing a cone six days ago."

It's been six days since my cat started wearing a cone. It's been six days since my cat started wearing one.

NOTE: The pronoun "one" is a better word choice than "a cone" because readers can infer the context.

TFor the first two days, she seemed like she was really feeling stressful,ed and ended up giving up on moving. For the first two days, she seemed like she was really feeling stressed and ended up giving up on moving.

You don't need a comma unless there is a full subject and verb after 'and.'

The first two days, she seemed like she was really feeling stressfuled, and ended up giving up on moving around. The first two days, she seemed like she was really feeling stressed, and ended up giving up on moving around.

The first two days, she seemed like she was really feeling stressfuled, and ended up giving up on moving. The first two days, she seemed like she was really feeling stressed, and ended up giving up on moving.

TDuring the first two days, she seemed like she was really feeling stressful, and ended up giving up movingreally stressful, but eventually ended up accepting the cone. During the first two days, she seemed really stressful, but eventually ended up accepting the cone.

She bumped into obstacles because of the cone around her neck obstructed her view whenever she tried moving. She bumped into obstacles because the cone around her neck obstructed her view whenever she tried moving.

Correct but a suggestion here to enhance the sentence.

SAt first, she bumped into obstacles because of the cone around her neck whenever she tried movingmoved. At first, she bumped into obstacles because of the cone around her neck whenever she moved.

Yesterday, I took her to the vet again, and her claws hasve gotten better. Yesterday, I took her to the vet again, and her claws have gotten better.

I'm not sure what you are referring to: the paw or the nails/claws?

Yesterday, I took her to the vet again, and was happy to learn that her claw has gotten better. Yesterday, I took her to the vet again, and was happy to learn that her claw has gotten better.

Her claw was infescted last week and she got an antibiotics injection at the vet. Her claw was infected last week and she got an antibiotic injection at the vet.

I think you want 'infected' rather than 'infested.' Infested is used for 'infested with rats' or something similar.

Her claw was infescted last week and she got an antibiotics injection at the vet. Her claw was infected last week and she got an antibiotics injection at the vet.

Her claw was infested last week and she gotreceived an antibiotics injection at the vet. Her claw was infested last week and she received an antibiotics injection at the vet.

ItThe wound hasn't completely recovered yet, but it looks much better. The wound hasn't completely recovered yet, but it looks much better.

sShe is still wearing the cone, but she looks like she is feeling well. She is still wearing the cone, but she looks like she is feeling well.

sShe is still wearing the cone, but she looks like she is feeling well. She is still wearing the cone, but she looks like she is feeling well.

sShe is still wearing the cone, but she looks like she is feeling well. She is still wearing the cone, but she looks like she is feeling well.

sShe is still wearing the cone, but she looks likehas to wear cone, but it seems she is feeling wellbetter. She still has to wear cone, but it seems she is feeling better.

My Cat is Getting Used to the Life With a Cone My Cat is Getting Used to Life With a Cone

You don't need the article "the" here.

My Cat is Getting Used to the Life With a Cone My Cat is Getting Used to Life With a Cone

My Cat is Getting Used to the Life With a Cone My Cat is Getting Used to Life With a Cone

My cat seems to be getting used theo life with a cone around her neck. My cat seems to be getting used to life with a cone around her neck.

This is correct. You could also say "My cat is adjusting to life . . ."

My cat seems to be getting used the life with a cone around her neck. My cat seems to be getting used life with a cone around her neck.

My cat seems to be getting used theo life with a cone around her neck. My cat seems to be getting used to life with a cone around her neck.

My cat seems to be getting used the life with a cone around her neck. My cat seems to be getting used life with a cone around her neck.