Is there a character map that I can use to access additional glyphs?

Yes, to access all of the glyphs in a font, select a text box, then click on the Character Map icon located next to the font style drop-down box in the tools panel. Select a glyph, then click Copy and then position your cursor where you want the glyph to be added. Paste the glyph into the text box, using CTRL/COMMAND + V.