tire vibrations?

i've been restoring my bike for the last couple of months and while restoring it i had to fix a leak in the front tire. to do this i bought that green slime stuff that is suppost to stop all slow leaks, but in doing so i think it may have done something to disrupt the balance to my front tire, but thats jsut my thoughts. whats happening is a loud humming noise will come from the front of the bike, starting at any speed and will start loudly without warning and without and pattern. but how it goes away does have a patter, to get to it stop, all i have to do is slow down, to maybe 15mph; that usually takes care of it. what i have also noticed is that as soon as the noise starts, the speedo jumps about 10mph ahead of itself and cannot stay at a constant speed no matter if the throttle is. so my plan of action is to get a tube for the tire, does anyone else disagree with this plan and think otherwise?