First, you're doing the most important thing in taking lessons. That will give you the BEST return on your investment. Your existing clubs, if they are cast, perimeter weighted clubs, are probably ok. As you said, they are Callaway knockoffs. BTW, the 3 and five woods in my bag are Knight brand that I bought from Sam's Club many years ago, for $29.95 each, and on the rare occasion that I hit them, they are fine. Now my driver is a TaylorMade R7 (425), and I love that club. It's really the only "name brand" club in my bag. My irons are a combination of custom made clubs I had made 10 years ago at a Raleigh golf shop and clubs I bought "over the phone" on trial eight years ago from Carbite, not a name brand outfit, but they work well for me, I like the look and feel of them, and I am not looking to replace them. They are "mid size" irons. I have never liked the look of the really big "over-sized" clubs, but that is personal preference.
If you like the Tommy Armour's and can get them for the cost of regripping, get them. Maybe they will be more consistent "club to club" and give you more confidence, and they are good clubs. You might find that they are a great next step for you game, now that you've taken your lessons. While the club manufacturer's come out with new models every year that hype their "improvements" that make them must have, unless you're a single digit handicapper, they won't help you much. The biggest improvement change happenned 25 or so years ago when the cast clubs came out, like the original Ping Eye irons, replacing forged blades. Changes since then have been in very small increments and mostly cosmetic in nature.
Different irons have varying "looks". Is the top line, what you see when you look down, thick or thin? Which do you prefer? I like the thinner line, while one of my friend likes the thick line and plays Callaway X16's, and another friend got new Mizuno's last year, after playing custom made "American Standard" clubs (they are better known for their toilets than they are for their golf clubs!) for almost 20 years, and he played just as well with those, even after all these years, as he does with the new clubs - and he's a 7 handicapper.
Of course, there is also the new "hybrid iron", which are replacing the lower irons in sets because they are supposedly easier to hit. I don't like them and I still carry 1 and 2 irons in my bag. I love my 2 iron and like my 1 iron, and don't like the hybrid I tried.
Good luck and enjoy!