After playing Skyrim for a long time, I bought Oblivion and I'm playing through it for the first time. Oblivion is much more difficult to me.

I can get through the beginning of the game fairly easily but once I get to around level 5-6, my character just seems helplessly gimped. It seems to me my character is just not leveling commesurate with the leveled mobs I fight. I'm playing an Imperial Assassin with the Thief birth sign. I'm putting points in agility, speed, and intelligence, with some in strength and endurance every other level. My attacks with bows and blade weapons do little damage to most mobs at this point and I have to hit things a million times to kill even the weakest mobs. I have to chain healing pots so much that I can't make enough to keep myself stocked because I can only make 4 pt healing pots as a Journeyman Alchemist right now.

I'm playing on the default difficulty. I really don't know what I'm doing wrong. Help.

It might help if you could provide a little more detail. What are your skill levels in bow, blade and sneak? With sneak of 25 or more, you should get a decent sneak damage bonus.

Are watching your fatigue? Your attacks do less damage when your fatigue is low.

Are you using poisons? At journeyman alchemy you can make some powerful poisons.

What types of enemies are you having the most trouble with? At level 5-6 you should be able to handle most enemies you meet on the road with your sword, as long as your blade skill is above 25, even if you are not wearing any armor at all.

Are you using the basic healing spell to heal yourself up after each battle?

Are you keeping your weapons repaired? They do less damage when worn. Same goes for armor.

And are you running any mods that tinker with the world leveling/scaling? There are some mods that can make the early levels much more challenging, especially if you wander into the wrong place.

Just keeping fiddling around, try not to do the main quest too much (damn dremoras...)

A few thoughts besides what Turija already said:

Putting points into attributes actually has very little effect on how much damage you do. Skill level, fatigue and equipment health & quality are all way, way bigger factors.

If you aren't keeping your fatigue up during battles you are going to take a million hits to kill something. I tend to brew custom potions with Restore Health + Restore Fatigue + Shield for melee combat personally.

Combat against mobs is supposed to be tough. Exponentially tougher than one on one battles.

Have you been upgrading your gear?

Poisons are also great for dealing with enemies, especially groups since a lot of times you can hit once and move on to the next one.

Since this is the first time you're playing the game you could also consider bumping the difficulty slider down a couple clicks.

If you need healing potions, conjurer dungeons tend to have lots, but they're also more likely to mob attack you than most.

Running is always an option.