Well that's an interesting dilemma. But you can overcome your limitation!
As you suggested you have two options:
Option one is to switch to lefty guitar so your right hand becomes your fretting hand. Option two is to learn to adapt your fingering to compensate for your handicap. Let's explore both options.
I don't see any reason why it would be any harder to learn to fret with your right hand to play a "left hand" guitar. Many left handed folks learn right handed guitar because they know right handed guitars are easier to come by and don't have to be special ordered and can be found used etc. So they learn to play right handed guitar from the beginning - which for them is like a right handed person learning left handed. I have never heard any complaints from the folks I have known who are left handed but play the guitars that right handed people play.
Either way you learn, you must train your brain to get your fingers to do very awkward and unnatural things and contort into strange shapes. I can't think of any reason why a right handed person would find this easier to do with the left hand and have often wondered who decided that right handed folks should use their left hand as the fretting hand to begin with.
The key may be in your ability to maintain a consistent strumming rhythm with your left hand and arm. If you can master some basic rhythmic in time strumming with your left hand, as easily as you can with your right hand, there is no reason you should expect the learning curve to be any different starting from ground zero - regardless of which hand you use for fretting. Of course, now is the time to make the change if you do go that route.
The other option is to learn to adapt. Certainly there will be some open chords that will be more difficult to play in the typical fashion if you can't bend the last knuckle in your index (first/trigger) finger. One that comes to mind is the C chord which is usually played with the index finger fretting the second string (b string - next to skinniest string) on the first fret.
One solution would be to learn to form most chords with your pinkie, ring finger and middle finger and leave off your index finger. Since the pinkie is usually the finger that most beginner's find to be the least controllable, most beginning guitar students tend to avoid using the pinkie in the beginning. But as you become more advanced, the pinkie becomes very important. So why not start developing it now.
Your inability to bend the fingertip knuckle will not impair your ability to play barre chords. And if you learn to play most open chords with the other three fingers, it will be easier for you to play barre chords which often require the use of the other three fingers. You will probably even find yourself making great use of the C shaped barre chords and D shaped Barre chords in addition to the more common E shaped and A shaped barre chords.
To play an A major chord in first position you can use a mini barre with your middle finger or ring finger - so you use just one finger to play it. I play a G chord with pinkie, ring and middle finger as a matter of course. I play an F chord as a barre chord with a straight index finger. I often play an E chord with my pinkie, ring and middle finger so I can simply slide that same shape up the fretboard to play other E shaped barre chords.
I think the most difficult challenge for you would be to try to play a C7 or G7 in open position without the ability to bend the finger tip knuckle of your first finger. So perhaps you might have to play those as barre chords on the occasions when you need to play a C7 or G7 in a song.
You will be able to make it work either way - if you have a strong enough desire! Remember that learning guitar takes a great deal of determination and commitment born out of a strong desire. That does not change whether you learn to fret with your left hand or right hand. And it does not change if you are forced to alter your fretting technique and fret some chords in a manner that some might call unconventional.
There are many examples of folks who have learned to play with only two fingers. I saw a YouTube vid of a guy playing with his toes. So if the desire is there, you will find a way to adapt.
I gave up guitar as a teenager because I broke my pinkie on my fretting hand and it grew back crooked and weaker. At the ripe old age of 40 I decided to try again - this time with more passion and desire and determination. I was able to overcome my limitation and learn to play quite well. I now get paid to play guitar and sing at local venues and private parties. I am so happy that I decided to give it another shot. There are a few chords I can't play like other folks but I have learned to substitute other chords or play a different fingering. It has not held me back.
Regardless of which direction you go from here - enjoy the journey. It will be worth the effort in the end.