You really need to have her checked by the vet.

Urinary infections can be very painful and need to be treated. If they have an infection like that, they don't always use something besides the litterbox every time, it may seem random to you. If it's a behavioural thing then your vet should be able to help you there also. Be sure to tell the vet about the other pets, her licking issues and her separation anxiety, that will help them narrow down her issues.

The longer this urinating on the bed is allowed to go on the more of a habit it can become to the point where it's difficult to break them of the habit. Hopefully in this case it's an easily treatable medical problem that has only been going on for a few days.

Living in a carrier is not much of a life for a cat, even if it does save on the mattress.

Other things to try:

Add one more litter box. Rule of the house is one litterbox per cat plus one.

Make sure the second litterbox is different than the original one. (ie; if your old one is high sided, get a low sided one. If your old one is hooded get a non hooded one.)

Don't put any liners or deoderizers in the extra box. Some cats learn to dislike those.

Put the extra litterbox in a different place. (ie; if the old one is downstairs, but new one upstairs. If old one is in bathroom, put one in a bedroom. etc)

Make sure neither litterbox is near something noisy (like a washer/dryer/furnace) where the noise may scare the kitty, and make sure it's not a very busy area of your home (like right near the main entrance door).

Put different litter in the new litterbox. (ie; if the old box had scented clumping litter, get a non clumping, non scented clay litter) Some cats learn to dislike a particular litter or scent, and sometimes companies change a formula in a litter you've been using for years and the cat may not approve of the change.

Scoop all litterboxes out once a day.

Keep at least 2-3 inches of litter in the box at all times.

At least once a week (for clay litter) or once a month (for clumping litter) dump out the box and wash it out with only hot water. Some cats don't like the smell of clorox/lysol/pinesol etc.

With other pets in the house, make sure they are not bothering the cat when she needs to use the litterbox (ie; blocking her from getting to it, or cornering her when she's in it)

Good luck.