Usually a throw out bearing noise will change when you engage/disengage the clutch. It will make noise with the clutch released but not engaged unless it's really bad.
A balancer replacement isn't too difficult, but you may have to remove the radiator to do it. Just remove the pulley, take the big center bolt out, use a balancer puller to remove. The balancer has a slot in it that goes over the woodruff key in the crank....line those up and install the new one with a balancer installer or a big hammer and a scrap piece of wood. The rest of the install is the reverse of removal. Tighten the crap out of the big bolt- it's usually torqued to around 100 ft-lb
As always though, if you aren't totally comfortable doing it, a shop will be happy to help.
1973 VW Karmann-Ghia first car
2009 Challenger R/T 6MT, Flowmaster, inTune daily driver
1977 CJ5 304, 3MT - under construction
And many in between!