Need help getting TM's

There are currently only three ways to get TMs. First, as raid rewards, secondly, from a very rare field research reward (win 3 raids), and third once a week from your research stamp box.

Luckily for you during the Water Festival, Sharpedo is one of the easiest Tier 3's to solo ever! It has the lowest defense of any evolved pokemon. If you see one around, it can be beaten really easily by people with only level 20 pokemon.

That being said, solo-ing a tier 3 gets you as much of chance for a TM as participating in a tier 5 raid and getting only 1 extra ball. The ideal way to farm for TMs would be joining a small raid group and getting many balls, but that sounds like it is not a reliable option. If you ever do happen to be doing a Tier 5, make sure to focus on DPS, not potion efficiency, increasing your chances of getting an extra ball, giving you extra rewards.

If you are a pure solo player, tier 3 raid is your best bet, still not guaranted 100% for TM, but the probability is better than tier 1-2
Sharpedo is easy, Vaporeon is doable, my lv 33 can solo it without weather boosted using 5 wild level 31-35 alolan exeggutor with grass move, with 1 Venusaur with FP, if your area is sunny a lot in PoGo it became more easier to do that
If you have 1 or 2 friends around your level playing PoGo, you can do tier 4 raid, must prepare your squad a little bit if you do duo T4,look for absol first, then tyranitar, then walrein. Look for cloudy weather ( easier and cheaper way is preparing a good machamp squad for your level) but trio is easy for all current T4, no need for cloudy weather..
2-3 trainer doing T4 imo is the best chance to get TM, as with legendary raid, people still want to do it with a lot of trainer, reducing the chance to get a better reward.
And shortmaning a legendaries need a good preparation of the counter squad..

Good luck with T3's! I haven't seen a charge TM in like the last 20 raids I've done and only one or two Fast TM's

I feel your pain. I had the same problem, more specifically a hopelessly long list of Pokemon to Charge TM. Like others here have said, the only solution is joining a local raid group or recruiting some friends and hitting T4/T5 raids. Once I got connected to a local Whats App group and started doing T4s and 5s, my CTM problem was gone within a week. What is most telling is that the people I raid with place almost no value on CTMs (to say nothing of Fast TMs) because they have such a big surplus.

Soloing T3's just doesn't cut it. I tried this for months; Your chances of getting a Charge TM are too slim, so you end up with too many good IV/CP candidates with the wrong moves and not enough TMs to go around.

At level 33, you will probably not yet have the mons you need for soloing Tier3 - at least most of them.

You need to find the local raid group and start doing legendary raids with them, while also focusing hard on leveling up and getting more stardust. Don't power stuff past lvl 31 without a damned good reason - I have very, very few lvl 32+ mons that weren't weatherboosted wild catches, and I only have two lvl 35+ - a blissey that I wanted to break 3k with, and a 100% C/DP machamp that I decided to take to lvl 40 because it's a 100% C/DP machamp.

You typically need 3~6 solid counters for a T3. I focus on Machamp T3's - but I have a lvl 31.5 98% lugia that really carries the team. I used to do a lvl 35 mediocre C/FS 'zam, Lugia, and 4 lvl 31 Espeons. Still couldn't do weather boosted C/DP Machamp until I got my C/SB Mew^2 last week.

I do T3's if I can find ones I can solo consistently, and otherwise use my free passes on T2's. Both rarely give TMs, though - those I mostly get from T5s.

Don't bust your ass leveling up Zappy. Zappy is good and all, but they're probably going to do the legendary beasts next, and Raiku is better than Zappy, generally speaking.

I understand how aggr(on)avating it must be to have no tm's.
My advice is to focus on high dps and don't ag(r)onize about potions, revives and tdo 😉

Most tier 3s are soloable with level 30 non-legendaries. Even if you stick to tier 2 raids for now, focus on building tier 3 solo teams.

For example, with the following team (all level 30), I find Machamp with Close Combat a walk in the park and Dynamic Punch doable:
1. Alakazam with Confusion + Future Sight
2. Alakazam with Psycho Cut + Future Sight
3. Espeon with Confusion + Future Sight
4. Gardevoir with Confusion + Dazzling Gleam
5. (Kantonian) Exeggutor with Confusion + Psychic
6. Dragonite with Dragon Tail + Hurricane
I only struggle with Heavy Slam, as I do not have a Metagross with Zen Headbutt + Psychic.

Gengar requires a little more thought into team selection depending on its charged moves. The good news is that the abovementioned Alakazam, Espeon and Metagross are also effective against Gengar. Add Gengar with Hex + Shadow Ball, Tyranitar with Bite + Crunch and Houndoom with Snarl + Foul Play. If you dodge well (easy for Focus Blast and Shadow Ball), you should not have a problem, though you may want to use a Rhydon with Mud Slap + Earthquake as an anchor against Sludge Bomb.

There are 2 field research tasks to earn TM's.

Win 3 raids = Fast TM
Use a Super Effective Charged attack in 5 Gym battles = Charge TM

Work on your tier 3 teams. The chances of TMs dropping are much better than tier 2. But you should only go for tier 3 if you know you have a good chance of beating it.

First off, Sharpedo is as easy as a tier 2. It hits a lot harder, but it has no defense and is soloable with level 15 fighting pokemon.
You mention your FP Venusaur but did you not catch any high level Alolan Exeggutors? With BS/SoB, they're phenomenal counters to Vaporeon and Starmie. Victreebel, Jolteon, Shiftry and Cacturne are some easier to get pokemon that can also contribute to the raid team at level 30+.
Machamp has a lot of viable counters and since it's a staple of the raid lineups, it's well worth investing effort into building a team. Abra or Eevee nests would be a good place to start, and in residential areas they are super common during the right weather.