If you're a farmer you probably won't go to the ER for a bug bite.  Having said that though you could perhaps get some dishwashing soap, put it in the hottest water you can stand and immerse you hand in that.  Or if you have epson salts use that rather than dish soap.

Keep doing that until you can get to a doctor on Monday.  I hate going to the ER every time some little thing happens because I know the cost.  If I weren't married I wouldn't have gone the last time so I am simply guessing as to whether or not you'd go.

Good luck.  If it's a brown recluse bite you could lose a significant portion of your hand before they get it under control.  (speaking from friends experience)