A melee alchemist is very viable but that doesn't appear to be what you're building.
The internal alchemist trades out very little and adds almost nothing. Add a melee alchemist archetype - vivisectionist and winged marauder are both compatible - and yes, you can mix it up in melee effectively. Vivisectionists can find a use for shuriken too.
If you want to use alchemical weapons though, you have the problem of drawing them rapidly and the problem that their damage/saves tends to be unimpressive, and you can't add precision damage to them. Even making them yourself you won't often use them past ~level 3. The grenadier archetype gets some use out of these but is not compatible with internal alchemist.
Really, a longspear works just fine. Get a +str mutagen and maybe add a buff and you're ready to go. You don't need to spend a feat on a ripsaw glaive.
Is this 15-point buy? What do you hope to gain from the Internal Alchemist archetype? You don't seem to have identified what exactly it is you want this character to do.
The obvious option for a melee alchemist is to pick up Feral Mutagen and use a bunch of natural attacks. Alchemists get enough buffs that you can really crank your Str up high. Two levels of Barbarian let you pick up a gore attack through Lesser Beast Totem (not to mention getting Str up even higher, though it may not be worth the delay in your extract progression), and you can get tentacles as secondary attacks through further discoveries as well. Helm of the Mammoth Lord gets you a gore attack for 8,500 gp and your head slot as well.
A reach weapon could also be a good option, similar to a reach Cleric. Spend your standard actions buffing/throwing bombs, then let people provoke AoOs when they come after you.
If you're going melee, you want to focus on Str, not Dex. Even if you want to throw things, your bombs don't require a high Dex because they are touch attacks and a Belt of Hurling will let you use STR to throw things once you can afford it. Beastmorph is a good archetype even if you don't go the feral mutagen route. I actually like the Power Attack/Furious Focus/Vital Strike combo for 3/4 BAB characters because your additional attacks aren't going to be hitting that often anyways. I also prefer a d10 weapon because it scales up to 2d8 and 3d8 with enlarge and Impact. I'm running an alchemist right now with Combine Extracts and Enlarge Person with Longarm that's quite fun.
You don't get those feats for free, you can take them in place of a discovery.
Bonus Feats: An internal alchemist can select Alertness, Extra Ki, Great Fortitude, Improved Critical (unarmed strike), Improved Initiative, Improved Unarmed Strike, Iron Will, Lighting Reflexes, Stunning Fist, or Weapon Focus (unarmed strike) in place of an alchemical discovery.
The Vivi is banned ofr PFS (and my group isn't fond of it either), I have to disagree about alchemical weapons, tangleburn bags, gel shards (AoE caltrops), liquid blades (you can pre poison them!), pellet grenades, holy water, those all seem pretty useful for awhile (we are currently level 9)The internal alchemist trades out very little and adds almost nothing. Add a melee alchemist archetype - vivisectionist and winged marauder are both compatible - and yes, you can mix it up in melee effectively. Vivisectionists can find a use for shuriken too.
If you want to use alchemical weapons though, you have the problem of drawing them rapidly and the problem that their damage/saves tends to be unimpressive, and you can't add precision damage to them. Even making them yourself you won't often use them past ~level 3. The grenadier archetype gets some use out of these but is not compatible with internal alchemist.
OK, no vivisectionist. Winged Marauder gets you a flying mount - if you're going to be throwing alchemical caltrops around this will be handy - and anyway you can have fun with Spirited Charge.
Tanglefoot/burn bags and gel shards are seriously inferior to battlefield control spells at this level. The damage from tangleburn, pellet grenades and holy water is insignificant especially since an internal alchemist trades away the feature which lets you add Int to non-bomb splash weapon damage. PF makes poison an expensive and weak idea. I'm not sure you've thought this through.
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I don't really want to be negative here, but natural attacks and body modifications are a melee alchemist's bread and butter. Trying to build an effective melee combatant without them is kind of like trying to swim upstream. Also, no level dips isn't helping either.
But, that being said, I don't think you can't build a decent character without them.
A one level dip in inspired blade swashbuckler would allow you to be a dexterous melee combatant, but if you want to stick with alchemist it'll be strength all the way. I'd consider stats closer to this:
STR 17
DEX 14
CON 14
INT 14
WIS 10
CHA 8
Don't worry too much about the light armor and only a +2 dex mod, you'll have barkskin and natural armor to make up for it.
I would suggest taking either the Ragechemist, or the Beastmorph archetypes, but neither are it isn't compatible with the Internal Alchemist if memory serves. So if you're dead set on the Internal Alchemist, I might just leave it at that. Though after getting your poison/disease immunity, I would consider taking the Master Chymist PrC, for a few levels of extracts you gain full BAB, more mutation per day, and a bonus to damage with simple and natural weapons.
Also, even though you can use them, I wouldn't suggest using alchemical weapons or poison very often, they're not going to be very effective compared to your bombs, and cost you GP you don't need to spend.
I strongly recommend against the Ragechemist archetype. An extra +2 Str is not worth the increased Int penalty and chance of unconsciousness, in my opinion.
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I strongly recommend against the Ragechemist archetype. An extra +2 Str is not worth the increased Int penalty and chance of unconsciousness, in my opinion.
Yeah, actually looking back on it, the ragechemist archetype isn't as good as I remember. I take back my endorsement of it. Was mostly looking for a boost to combat abilities that didn't include beast shape/ natural attack type boosts.
Maybe mutagenic mauler for brawlers would be more to the OP's speed. Seems to fit better.