Could I get injured pulling a hoyer lift loaded with 200 pound patient?

You aren't supposed to be moving the lift with someone on it, it is strictly a lift to help transfer from bed to chair, from chair to toilet or shower bench etc.

Pretty obviously, yes you could. Never twist your back at the same time as you are pulling or bending.

English;
Yes, you can suffer an injury. If you need to move a patient from the bed to the chair or commode or another area, do so very carefully. But, it's very difficult to move a patient in a Hoyer on thick carpeting. Don't move the patient if you can't move them EASILY. DON'T move them if it is very difficult to do so, or you may have an accident.

Español;
Si, tú te puedes lastimar. Sí tú necesitas mover el paciente de la cama a la silla ó inodoro portable ó un otro lugar, haslo con mucho cuidado. Pero, es muy deficil a mover un paciente con un Hoyer sobre la alfombra gruesa. No muevas el paciente si no puedes empujar FACILMENTE. NO muevas si hay mucho dificultad porque tú ó tu paciente pueden sufrir un accidente.

Usually a Hoyer lift is not supposed to be rolled across the room.  However, some nursing staff in long term care facilities use the Hoyer lift to "carry" a resident from the bed to a chair located across the room (4-5 feet away) instead of transferring the resident to a wheelchair, pushing the wheelchair to the recliner or chair that the resident is going to sit in, and then using the Hoyer lift again to transfer the resident from the wheelchair to the recliner.  Or use the Hoyer lift to "carry" a resident into a bathroom that is too small to accommodate the wheelchair and the Hoyer lift at the same time.

Here are a couple of instructional manuals on "How to Use a Hoyer Lift" that you can "Copy & Paste" the URL to your browser.

http://www.cdss.ca.gov/agedblinddisabled/res/VPTC2/4%20Care%20for%20the%20Caregiver/How_to_Use_a_Hoyer_Lift.pdf

https://www.wikihow.com/Use-a-Hoyer-Lift states “If you are moving to another room, slowly adjust the swivel bar so the user is facing you as you move the lift.” 

IF you MUST roll the Hoyer lift from one place to another place within a room or to another room, I would suggest that the patient’s family purchase some linoleum flooring to cover the carpet so that the wheels of the Hoyer lift can roll easily and not get caught by the carpet fibers.

Sometimes when you take care of a person at home, you have to improvise or modify how you use equipment because of constraints in the amount of space to work in.

The whole point of a lift is to make caregiving easier, if it isn't doing that what is the point? Although it may seem simpler to raise the person from the bed and then push the lift to wherever if it is danged near impossible to move the lift you've really just substituted one problem for another. Somebody needs to come up with a better method, here are some ideas:

-making multiple transfers, which would be more time consuming but you would then be repositioning the lift without the person on it

-laying a firm surface over the carpet so the lift can move more easily (I'm not confident linoleum alone would be sufficient because the lift would still sink into the softer carpet below)

-lifting the carpet

-rearranging the room so moving the lift isn't necessary

Don't accept the status quo because you fear losing your job, you won't be earning anything for a long time if you are injured.

I never push my husband in the Hoyer farther than a foot. Those lifts are nearly impossible to push on a wood or tile floor with the person swinging in the sling. On carpeting? No way. Not safe. It’s not meant to transport people from one room to another or even across a room.