Welcome to the world of amplified harmonica playing !!Yes, your amp is most likely the problem, but just cupping your hands around any type of mic is asking for feeback. You should have less problems with a bigger amp, but feedback will never completely go away.
Read this section first and then ask your new questions back here-
http://www.harmonicalessons.com/members/mics.php
Here's some more info-
"AVOIDING FEEDBACK; HOW TO GET AN OVERDRIVEN SOUND"
http://www.harmonicalessons.com/members/dcforum/DCForumID4/56.html#1
"DG MIC/AMP SETUPS FOR LIVE AND STUDIO PLAYING"
http://www.harmonicalessons.com/members/dcforum/DCForumID4/44.html#9
Play on,
Dave Gage