I would real suggests the left hand rem sps compact 20" barrel shorter length of pull in 7mm/08.

I am a left handed shooter as well and until recently readily finding left handed rifles was difficult and painfully expensive when you did find one. I had been relegated to shooting lever or auto-loader'f for many a year. I now have a safe full of left handed rifles thanks to companies like Remington, Savage, Browning and Tikka that have made left handed rifles more readily available. To date though Tikka and Savage seem to be the most available for lefties and just about every shop has a couple on the shelf. I'd highly recommend that you look at the Tikka T3 Lite rifles...I have one n Stainless chambered in 270WSM and it handles very nicely, light, wonderful adjustable trigger, detachable mag, very accurate (first 3 shots out of the box were sub-MOA with factory ammo), and available in a variety of light recoiling calibers like .243, 7-08, 25-06...all great deer calibers and easy to find ammo for. I also like my Savage 11 in 7-08...nice adjustable trigger (just not as nice as the Tikka), handles quickly, accurate (not as accurate as the Tikka out of the box), detachable mag...but they are a little less $ than the Tikka...can't go wrong with either.

I was going to remark, to wait for EMT to "reply" !

I'd try a h&r handi rifle in a 243 or 7mm-08

Well I live in Indiana and the regulations are as follows for rifle cartridges and handgun cartridges. So it does further limit me.
Rifles with cartridges that fire a bullet of .357-inch diameter or larger; have a minimum case length of 1.16 inches; and have a maximum case length of 1.8 inches are legal to use only during the deer firearms and special antlerless seasons. Some cartridges legal for deer hunting include the .357 Magnum, .38-.40 Winchester, .41 Magnum, .41 Special, .44 Magnum, .44 Special, .44-.40 Winchester, .45 Colt, .454 Casull, .458 SOCOM, .475 Linebaugh, .480 Ruger, .50 Action Express, .500 S&W, .460 Smith & Wesson, .450 Bushmaster, and .50 Beowulf.
Some handgun cartridges that are legal for deer hunting include .357 Magnum, .41 Magnum, .44 Magnum, .44 Special, .45 Colt, .45 Long Colt, .45 Winchester Magnum, .35 Remington and .357 Herrett.

I am not real savvy on to many firearms. Mostly fired shotguns and a few handguns. The kick of my shotguns are a real problem and so my search continues.

Lighter Calibers that would be easier on You as far as recoil and the Remington Managed Recoil shells will make them even lighter or a caliber that has too much recoil easier for You to use!
.243 light on recoil
30-30 light on recoil
7mm-08 easy on recoil and the Managed recoil shells would make it even lighter and easier to use!
.270,30-06,25-06 .308 etc all with more felt recoil but much easier on the recoil when using the Managed Recoil bullets !If You already have a larger caliber Rifle and want to save money just buy the Remington bullets and You saved a lot of money on keeping the Rifle You have and the point of impact may only be an inch lower than the original bullets You shoot before saving time and cost on adjusting Your scope!

Something is missing from that text as to calibers legal for deer in Indiana....I'd suggest some additional research as when i hunted there years ago with a friend I know I used a .270 Win...(I think it was legal...LOL

What ever gun you choose and with the handicap you are dealing with I strongly suggest a shooting stick such as a primos trigger stick.
it will greatly improve comfort and accuracy

That is dirrectly guoted from the Indiana dnr website

http://www.eregulations.com/indiana/...r-regulations/

I have never know that a .270 was legal. Indiana is also very frequently changing the rules. Sometimes for the better sometimes not.

However I don't think I will be able to participate in the special antlerless season this year. I kneck is hurting me so badly and I just don't want to further agrivate it before Tax season kicks off in a couple weeks. I won't have time to take to many days off to go to the Dr.

***No further research is needed on the IN requirements. It's as posted in the above link and nothing smaller than a .35 caliber has ever been allowed there (I grew up there), so you were lucky you didn't get caught with that
.270 during deer season.