If you have a warrant, you can get arrested anytime you go anywhere, but is it likely to happen? No, unless someone does a criminal background or warrant check. Hosp is probably not going to run a warrant check. Go get medical help. Then schedule a warrant quash hearing with the court so you are not living in fear.
If you really do have an outstanding warrant for your arrest, you run the risk of being arrested...wherever you are. That said, hospitals are not in the habit of running warrant checks on people who come in for treatment. Overall, this risk of you being arrested is probably outweighed by your need for medical attention. Once you are well enough, you should retain an attorney to help you take care of the warrant. More often than not, it is usually dealt with in a relatively simple manner, especially if the warrant was issued because you failed to appear for court in a minor criminal matter, failure to provide proof of completion of community service hours/payment of restitution/court ordered treatment etc. Take care of yourself, then take care of the outstanding warrant.