Consider not worrying about it and just continuing on. At Adventurer's League, tables are divided by tiers, and while new players (or players with new characters) start at level 1, that same table can have players from level 1 to 4. I know you're not doing Aventurer's League, but the same "tier" concept still applies — see chapter 1 in the DMG.

In fact, I've specifically played (parts of) Lost Mine of Phandelver both as a 1st-level character when there were also 4th-level characters at the table, and as a 4th-level character when there were others at 1st level. In both cases, it was fine. The higher-level characters took more risk and did some covering for the lower-level ones, but (especially once over the jump from 1st to 2nd), there wasn't even much of a real-world issue of the higher-level characters taking up too much game spotlight.

You mention that the module is meant for 1st level characters, but actually it's meant to take characters from 1st to 5th. Think of it as a first tier adventure. Starting at 4th certainly makes things easier, but... it'll all work out. Particularly, consider that it takes 2700 experience points to get to 4th level, but 6500 (that is, 3800 more) to get to 5th. Your other players will catch up, and everything will be fine.

You should be able to play this

It is in no way optimal, but it's certainly possible to play this kind of character, and it will provide you with great roleplaying opportunities. A crippled fighter who uses what little Druidic magic he knows to get by where his physical form can no longer help is a great concept.

As you've already determined, having a low strength and a low dex, you are stuck with having terrible AC unless you wear heavy armor, which has a strength requirement unless it's a mithral armor. You will be able to use a shield alongside a club (heavy stick) for a bonus +2 AC, which means you'll be a fairly tanky character if you don't dump-stat your con as well for the theme.

You will also need to use your bonus action every minute to cast Shillelagh or you'll struggle to hit anything, but once you've done that, you're essentially just using a one-handed longsword, which is a perfectly viable build. You'll be weak to dispell magic and anti-magic zones, but in all honesty, if somebody is going to cast that to dispell your cantrip, they've wasted a spellslot.

For your once per day spell from Magic Initiate, you might consider Absorb Elements. Because you'll be dump-statting your dexterity, there's a decent chance you're going to fail dexterity saves as you are not proficient in those, and a well-timed Absorb Elements might well save you 10+ damage from a spell.

For your other cantrip options besides Shillelagh, you might want some way to 'close distance' or attack from a range, for those situations where your movement (especially when you're slowed down by armor) can't get you near enough to the enemy. With a decent wisdom modifier, your Thorn Whip would allow you pull enemies closer reasonably well. Gust might be useful to push enemies over edges from a distance or push unattended weapons around, allowing you to be more useful from a range than your slow speed would normally allow.

So in conclusion, is this going to be the strongest character at your table? Almost certainly not.

Is it going to be unplayable? I don't think so. I think that once you find Mithral Armor or find some other way to get a decent AC, your character will be perfectly viable in anything but a heavily min/maxed environment.