Your heartrate may be high because you are out of shape,
and anxiety/stress can easily cause the heartrate to increase because then the body releases adrenalin.
Adrenalin is like ultra-mega-coffee.
If you want to heal your stress and anxiety, i do not recommend pharmaceuticals.
benzo's and ssri's have many side-effects, effectively once u want to withdraw from them. i suggest u read horror stories from places like paxilprogress.org or benzoisland.org if you or one of your loved ones ever decide to use pharmaceutical drugs to combat depression or anxiety.
i recommend relaxation techniques such as vipassana.
http://www.urbandharma.org/udharma4/mpe.html
there you can read a free book that contains all the information you need to learn to transform anxiety and depression into peace and happiness.
it takes a couple of months to adjust your behavior but after 1 or 2 years you will have made incredible progress.
some people fail at adjusting their behavior even though they have made a serious effort for a period of time that is long enough for it to start to work,
through techniques such as vipassana meditation.
for these people, as well as people who experience lifethreatening depression or anxiety,
pharmaceutical drugs may be the best option... but they should only be used for as brief periods as possible.
if it's not even necessary, don't bother going on them.
it's not worth the potential side-effects.
if it makes you feel any better... when i'm not taking pharmaceuticals
i sometimes have a heartrate of 120 standing,
and 140 walking or slow bicycling.
The exercise rates actually seem normal to me. Those are in the target ranges for your age. Mine will response similarly, I'll be up to 120 in about 2 minutes of warm-up. If I run or pedal fast it'll go up to 160-170.
Not sure what could be casing the at rest tach. When there is no concern or cause it's labeled "inappropriate sinus tachycardia" or IST. Give that a search
I learned a hard lesson about exercise recently. Start off very slow if you're out of shape. Be consistent and there's no need to set world records.