You may want to look into Solid Phase Micro-Extraction (SPME). It is a fast, solventless alternative to conventional sample extraction techniques. In SPME, analytes establish equilibrium with the sample matrix, in the headspace above the sample, or directly in the stirred aqueous sample. The polymer-coated fused silica fiber, can then be desorbed from the fiber to the chromatography column.
Most chromatography columns and stationary phases are incompatible with water injections. because of its polarity, boiling point and reactivity with bonded silica phases.
The aqueous solution analysis in GC-FID is very difficult and not recommended. However, in same GC you can analyze the aqueous sample by injecting into the headspace. Nowadays, GC are equipped with headspace, specially to analyse water sample. Moreover, you can concentrate the sample by several extraction techniques in conventional GC if it contains less amount then dry the sample with anhydrous sodium sulphate.
I am in general agreement with the other respndants but would add the following in response to your headline question.
1/ Many columns will be destroyed by repeated aqueous injection. The Carbowax column you are using should be OK but if you or any other readers try this with typical non-polar columns it could be expensive.
2/Whilst the FID and many other GC detectors have very good absolute sensitivity, in that they can detect a very low mass entering the detector,their relative sensitivity is not so impressive. This is because the volume you can put onto a column is very limited. Particularly if some of the volatile organic components in your aqueous sample are high relative to the compounds of interest you will soon start to see the chromatography degrade if you overload the column.
3/.The solvent or solid phase extraction steps often serve to do an initial separation from potential interferents.
30 years ago we were happily injecting filtered beer onto packed Carbowax 20M columns for determination of ethanol. A nice simple arrangement with lots of stationary phase which could stand up to water and the ethanol i was measuring was between 3-5%. No problem. But I would not have tried it with a typical environmental sample.
So to summarise, if you have the right column, with a simple matrix and with your analytes at reasonable concentration it may work. but it really should not be your first thought. Purge and trap or SPME (as mentioned by Steve) are now avaailable at reasonable cost, particularly the SPME. The use of headspace analysis mentioned above is also an option but the analyte has to have reasonable volatility.
We do this at our lab. One thing you really want to watch out for is the amount you are injecting due to expansion volume of water in the GC inlet. The expansion volume of water is almost 10x that of n-hexane, which will cause backflash and contamination if you are injecting 1-2uL.This may be why you are having baseline issues. The expansion volume of water and the size of your inlet liner is critical when doing aqueous injections. Base the amount injected on the internal volume of your inlet liner (for water 0.5uL). Once you have figured that out you should have much more reproducible results. Also - watch the higher temperature range when using WAX columns, they are typically lower than normal capillary GC columns. Agilent has a good write up of this..... starting on page 20 of the attached link... good luck!