Okay if it's on solid you have a problem which requires attention and you can continue to drive the vehicle until you can get it looked at. If it ever flashes while driving don't continue to drive it.
You'll need to get the computer scanned to find out what's wrong. Most auto parts stores will do this for you OR rent you the scanner to scan it yourself.
If you reply here with the code I can help you further to figure out what the problem is.

Hi Jesse,

That code is for the primary heated O2 sensor heater malfunction. In order to get the O2 sensor working faster to reduce cold start emissions the O2 sensors on newer Hondas have an internal heater inside. It's similar to a toaster coil. It warms up the O2 sensor faster basically because it only works when it's hot.
So this is a really easy fix. You replace the O2 sensor and the problem should go away. The primary is the one in the front or the first one. You don't have to get a Honda OEM O2 sensor (although I recommend it) but you can get a cheaper Denso brand direct fit O2 sensor. Don't get a Bosch or an O2 that you have to cut the wires and butt connect them back up. Those will not work well on a Honda and will set codes. Hondas have very precise fuel control direct fit Denso is about the only thing I will use besides OEM Honda replacement O2's. Denso is the OEM supplier originally so it's the closest thing to OEM.

Hope that helps.

Hi Jesse,

In order to tell you exactly where it is you need to tell me the engine number on the block (which is on the front to the left of the exhaust manifold) and if it's a manual or automatic transmission. They made about 5 different version Civic's in 98.
To answer your second question it's okay to drive it until you can get around to replacing it. It's not going to get worse or cause an issue that will damage anything else.